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Statistics By Jim

Making statistics intuitive

One-Tailed and Two-Tailed Hypothesis Tests Explained

By Jim Frost 60 Comments

Choosing whether to perform a one-tailed or a two-tailed hypothesis test is one of the methodology decisions you might need to make for your statistical analysis. This choice can have critical implications for the types of effects it can detect, the statistical power of the test, and potential errors.

In this post, you’ll learn about the differences between one-tailed and two-tailed hypothesis tests and their advantages and disadvantages. I include examples of both types of statistical tests. In my next post, I cover the decision between one and two-tailed tests in more detail.

What Are Tails in a Hypothesis Test?

First, we need to cover some background material to understand the tails in a test. Typically, hypothesis tests take all of the sample data and convert it to a single value, which is known as a test statistic. You’re probably already familiar with some test statistics. For example, t-tests calculate t-values . F-tests, such as ANOVA, generate F-values . The chi-square test of independence and some distribution tests produce chi-square values. All of these values are test statistics. For more information, read my post about Test Statistics .

These test statistics follow a sampling distribution. Probability distribution plots display the probabilities of obtaining test statistic values when the null hypothesis is correct. On a probability distribution plot, the portion of the shaded area under the curve represents the probability that a value will fall within that range.

The graph below displays a sampling distribution for t-values. The two shaded regions cover the two-tails of the distribution.

Plot that display critical regions in the two tails of the distribution.

Keep in mind that this t-distribution assumes that the null hypothesis is correct for the population. Consequently, the peak (most likely value) of the distribution occurs at t=0, which represents the null hypothesis in a t-test. Typically, the null hypothesis states that there is no effect. As t-values move further away from zero, it represents larger effect sizes. When the null hypothesis is true for the population, obtaining samples that exhibit a large apparent effect becomes less likely, which is why the probabilities taper off for t-values further from zero.

Related posts : How t-Tests Work and Understanding Probability Distributions

Critical Regions in a Hypothesis Test

In hypothesis tests, critical regions are ranges of the distributions where the values represent statistically significant results. Analysts define the size and location of the critical regions by specifying both the significance level (alpha) and whether the test is one-tailed or two-tailed.

Consider the following two facts:

  • The significance level is the probability of rejecting a null hypothesis that is correct.
  • The sampling distribution for a test statistic assumes that the null hypothesis is correct.

Consequently, to represent the critical regions on the distribution for a test statistic, you merely shade the appropriate percentage of the distribution. For the common significance level of 0.05, you shade 5% of the distribution.

Related posts : Significance Levels and P-values and T-Distribution Table of Critical Values

Two-Tailed Hypothesis Tests

Two-tailed hypothesis tests are also known as nondirectional and two-sided tests because you can test for effects in both directions. When you perform a two-tailed test, you split the significance level percentage between both tails of the distribution. In the example below, I use an alpha of 5% and the distribution has two shaded regions of 2.5% (2 * 2.5% = 5%).

When a test statistic falls in either critical region, your sample data are sufficiently incompatible with the null hypothesis that you can reject it for the population.

In a two-tailed test, the generic null and alternative hypotheses are the following:

  • Null : The effect equals zero.
  • Alternative :  The effect does not equal zero.

The specifics of the hypotheses depend on the type of test you perform because you might be assessing means, proportions, or rates.

Example of a two-tailed 1-sample t-test

Suppose we perform a two-sided 1-sample t-test where we compare the mean strength (4.1) of parts from a supplier to a target value (5). We use a two-tailed test because we care whether the mean is greater than or less than the target value.

To interpret the results, simply compare the p-value to your significance level. If the p-value is less than the significance level, you know that the test statistic fell into one of the critical regions, but which one? Just look at the estimated effect. In the output below, the t-value is negative, so we know that the test statistic fell in the critical region in the left tail of the distribution, indicating the mean is less than the target value. Now we know this difference is statistically significant.

Statistical output from a two-tailed 1-sample t-test.

We can conclude that the population mean for part strength is less than the target value. However, the test had the capacity to detect a positive difference as well. You can also assess the confidence interval. With a two-tailed hypothesis test, you’ll obtain a two-sided confidence interval. The confidence interval tells us that the population mean is likely to fall between 3.372 and 4.828. This range excludes the target value (5), which is another indicator of significance.

Advantages of two-tailed hypothesis tests

You can detect both positive and negative effects. Two-tailed tests are standard in scientific research where discovering any type of effect is usually of interest to researchers.

One-Tailed Hypothesis Tests

One-tailed hypothesis tests are also known as directional and one-sided tests because you can test for effects in only one direction. When you perform a one-tailed test, the entire significance level percentage goes into the extreme end of one tail of the distribution.

In the examples below, I use an alpha of 5%. Each distribution has one shaded region of 5%. When you perform a one-tailed test, you must determine whether the critical region is in the left tail or the right tail. The test can detect an effect only in the direction that has the critical region. It has absolutely no capacity to detect an effect in the other direction.

In a one-tailed test, you have two options for the null and alternative hypotheses, which corresponds to where you place the critical region.

You can choose either of the following sets of generic hypotheses:

  • Null : The effect is less than or equal to zero.
  • Alternative : The effect is greater than zero.

Plot that displays a single critical region for a one-tailed test.

  • Null : The effect is greater than or equal to zero.
  • Alternative : The effect is less than zero.

Plot that displays a single critical region in the left tail for a one-tailed test.

Again, the specifics of the hypotheses depend on the type of test you perform.

Notice how for both possible null hypotheses the tests can’t distinguish between zero and an effect in a particular direction. For example, in the example directly above, the null combines “the effect is greater than or equal to zero” into a single category. That test can’t differentiate between zero and greater than zero.

Example of a one-tailed 1-sample t-test

Suppose we perform a one-tailed 1-sample t-test. We’ll use a similar scenario as before where we compare the mean strength of parts from a supplier (102) to a target value (100). Imagine that we are considering a new parts supplier. We will use them only if the mean strength of their parts is greater than our target value. There is no need for us to differentiate between whether their parts are equally strong or less strong than the target value—either way we’d just stick with our current supplier.

Consequently, we’ll choose the alternative hypothesis that states the mean difference is greater than zero (Population mean – Target value > 0). The null hypothesis states that the difference between the population mean and target value is less than or equal to zero.

Statistical output for a one-tailed 1-sample t-test.

To interpret the results, compare the p-value to your significance level. If the p-value is less than the significance level, you know that the test statistic fell into the critical region. For this study, the statistically significant result supports the notion that the population mean is greater than the target value of 100.

Confidence intervals for a one-tailed test are similarly one-sided. You’ll obtain either an upper bound or a lower bound. In this case, we get a lower bound, which indicates that the population mean is likely to be greater than or equal to 100.631. There is no upper limit to this range.

A lower-bound matches our goal of determining whether the new parts are stronger than our target value. The fact that the lower bound (100.631) is higher than the target value (100) indicates that these results are statistically significant.

This test is unable to detect a negative difference even when the sample mean represents a very negative effect.

Advantages and disadvantages of one-tailed hypothesis tests

One-tailed tests have more statistical power to detect an effect in one direction than a two-tailed test with the same design and significance level. One-tailed tests occur most frequently for studies where one of the following is true:

  • Effects can exist in only one direction.
  • Effects can exist in both directions but the researchers only care about an effect in one direction. There is no drawback to failing to detect an effect in the other direction. (Not recommended.)

The disadvantage of one-tailed tests is that they have no statistical power to detect an effect in the other direction.

As part of your pre-study planning process, determine whether you’ll use the one- or two-tailed version of a hypothesis test. To learn more about this planning process, read 5 Steps for Conducting Scientific Studies with Statistical Analyses .

This post explains the differences between one-tailed and two-tailed statistical hypothesis tests. How these forms of hypothesis tests function is clear and based on mathematics. However, there is some debate about when you can use one-tailed tests. My next post explores this decision in much more depth and explains the different schools of thought and my opinion on the matter— When Can I Use One-Tailed Hypothesis Tests .

If you’re learning about hypothesis testing and like the approach I use in my blog, check out my Hypothesis Testing book! You can find it at Amazon and other retailers.

Cover image of my Hypothesis Testing: An Intuitive Guide ebook.

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June 26, 2022 at 12:14 pm

Hi, Can help me with figuring out the null and alternative hypothesis of the following statement? Some claimed that the real average expenditure on beverage by general people is at least $10.

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February 19, 2022 at 6:02 am

thank you for the thoroughly explanation, I’m still strugling to wrap my mind around the t-table and the relation between the alpha values for one or two tail probability and the confidence levels on the bottom (I’m understanding it so wrongly that for me it should be the oposite, like one tail 0,05 should correspond 95% CI and two tailed 0,025 should correspond to 95% because then you got the 2,5% on each side). In my mind if I picture the one tail diagram with an alpha of 0,05 I see the rest 95% inside the diagram, but for a one tail I only see 90% CI paired with a 5% alpha… where did the other 5% go? I tried to understand when you said we should just double the alpha for a one tail probability in order to find the CI but I still cant picture it. I have been trying to understand this. Like if you only have one tail and there is 0,05, shouldn’t the rest be on the other side? why is it then 90%… I know I’m missing a point and I can’t figure it out and it’s so frustrating…

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February 23, 2022 at 10:01 pm

The alpha is the total shaded area. So, if the alpha = 0.05, you know that 5% of the distribution is shaded. The number of tails tells you how to divide the shaded areas. Is it all in one region (1-tailed) or do you split the shaded regions in two (2-tailed)?

So, for a one-tailed test with an alpha of 0.05, the 5% shading is all in one tail. If alpha = 0.10, then it’s 10% on one side. If it’s two-tailed, then you need to split that 10% into two–5% in both tails. Hence, the 5% in a one-tailed test is the same as a two-tailed test with an alpha of 0.10 because that test has the same 5% on one side (but there’s another 5% in the other tail).

It’s similar for CIs. However, for CIs, you shade the middle rather than the extremities. I write about that in one my articles about hypothesis testing and confidence intervals .

I’m not sure if I’m answering your question or not.

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February 17, 2022 at 1:46 pm

I ran a post hoc Dunnett’s test alpha=0.05 after a significant Anova test in Proc Mixed using SAS. I want to determine if the means for treatment (t1, t2, t3) is significantly less than the means for control (p=pathogen). The code for the dunnett’s test is – LSmeans trt / diff=controll (‘P’) adjust=dunnett CL plot=control; I think the lower bound one tailed test is the correct test to run but I’m not 100% sure. I’m finding conflicting information online. In the output table for the dunnett’s test the mean difference between the control and the treatments is t1=9.8, t2=64.2, and t3=56.5. The control mean estimate is 90.5. The adjusted p-value by treatment is t1(p=0.5734), t2 (p=.0154) and t3(p=.0245). The adjusted lower bound confidence limit in order from t1-t3 is -38.8, 13.4, and 7.9. The adjusted upper bound for all test is infinity. The graphical output for the dunnett’s test in SAS is difficult to understand for those of us who are beginner SAS users. All treatments appear as a vertical line below the the horizontal line for control at 90.5 with t2 and t3 in the shaded area. For treatment 1 the shaded area is above the line for control. Looking at just the output table I would say that t2 and t3 are significantly lower than the control. I guess I would like to know if my interpretation of the outputs is correct that treatments 2 and 3 are statistically significantly lower than the control? Should I have used an upper bound one tailed test instead?

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November 10, 2021 at 1:00 am

Thanks Jim. Please help me understand how a two tailed testing can be used to minimize errors in research

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July 1, 2021 at 9:19 am

Hi Jim, Thanks for posting such a thorough and well-written explanation. It was extremely useful to clear up some doubts.

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May 7, 2021 at 4:27 pm

Hi Jim, I followed your instructions for the Excel add-in. Thank you. I am very new to statistics and sort of enjoy it as I enter week number two in my class. I am to select if three scenarios call for a one or two-tailed test is required and why. The problem is stated:

30% of mole biopsies are unnecessary. Last month at his clinic, 210 out of 634 had benign biopsy results. Is there enough evidence to reject the dermatologist’s claim?

Part two, the wording changes to “more than of 30% of biopsies,” and part three, the wording changes to “less than 30% of biopsies…”

I am not asking for the problem to be solved for me, but I cannot seem to find direction needed. I know the elements i am dealing with are =30%, greater than 30%, and less than 30%. 210 and 634. I just don’t know what to with the information. I can’t seem to find an example of a similar problem to work with.

May 9, 2021 at 9:22 pm

As I detail in this post, a two-tailed test tells you whether an effect exists in either direction. Or, is it different from the null value in either direction. For the first example, the wording suggests you’d need a two-tailed test to determine whether the population proportion is ≠ 30%. Whenever you just need to know ≠, it suggests a two-tailed test because you’re covering both directions.

For part two, because it’s in one direction (greater than), you need a one-tailed test. Same for part three but it’s less than. Look in this blog post to see how you’d construct the null and alternative hypotheses for these cases. Note that you’re working with a proportion rather than the mean, but the principles are the same! Just plug your scenario and the concept of proportion into the wording I use for the hypotheses.

I hope that helps!

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April 11, 2021 at 9:30 am

Hello Jim, great website! I am using a statistics program (SPSS) that does NOT compute one-tailed t-tests. I am trying to compare two independent groups and have justifiable reasons why I only care about one direction. Can I do the following? Use SPSS for two-tailed tests to calculate the t & p values. Then report the p-value as p/2 when it is in the predicted direction (e.g , SPSS says p = .04, so I report p = .02), and report the p-value as 1 – (p/2) when it is in the opposite direction (e.g., SPSS says p = .04, so I report p = .98)? If that is incorrect, what do you suggest (hopefully besides changing statistics programs)? Also, if I want to report confidence intervals, I realize that I would only have an upper or lower bound, but can I use the CI’s from SPSS to compute that? Thank you very much!

April 11, 2021 at 5:42 pm

Yes, for p-values, that’s absolutely correct for both cases.

For confidence intervals, if you take one endpoint of a two-side CI, it becomes a one-side bound with half the confidence level.

Consequently, to obtain a one-sided bound with your desired confidence level, you need to take your desired significance level (e.g., 0.05) and double it. Then subtract it from 1. So, if you’re using a significance level of 0.05, double that to 0.10 and then subtract from 1 (1 – 0.10 = 0.90). 90% is the confidence level you want to use for a two-sided test. After obtaining the two-sided CI, use one of the endpoints depending on the direction of your hypothesis (i.e., upper or lower bound). That’s produces the one-sided the bound with the confidence level that you want. For our example, we calculated a 95% one-sided bound.

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March 3, 2021 at 8:27 am

Hi Jim. I used the one-tailed(right) statistical test to determine an anomaly in the below problem statement: On a daily basis, I calculate the (mapped_%) in a common field between two tables.

The way I used the t-test is: On any particular day, I calculate the sample_mean, S.D and sample_count (n=30) for the last 30 days including the current day. My null hypothesis, H0 (pop. mean)=95 and H1>95 (alternate hypothesis). So, I calculate the t-stat based on the sample_mean, pop.mean, sample S.D and n. I then choose the t-crit value for 0.05 from my t-ditribution table for dof(n-1). On the current day if my abs.(t-stat)>t-crit, then I reject the null hypothesis and I say the mapped_pct on that day has passed the t-test.

I get some weird results here, where if my mapped_pct is as low as 6%-8% in all the past 30 days, the t-test still gets a “pass” result. Could you help on this? If my hypothesis needs to be changed.

I would basically look for the mapped_pct >95, if it worked on a static trigger. How can I use the t-test effectively in this problem statement?

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December 18, 2020 at 8:23 pm

Hello Dr. Jim, I am wondering if there is evidence in one of your books or other source you could provide, which supports that it is OK not to divide alpha level by 2 in one-tailed hypotheses. I need the source for supporting evidence in a Portfolio exercise and couldn’t find one.

I am grateful for your reply and for your statistics knowledge sharing!

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November 27, 2020 at 10:31 pm

If I did a one directional F test ANOVA(one tail ) and wanted to calculate a confidence interval for each individual groups (3) mean . Would I use a one tailed or two tailed t , within my confidence interval .

November 29, 2020 at 2:36 am

Hi Bashiru,

F-tests for ANOVA will always be one-tailed for the reasons I discuss in this post. To learn more about, read my post about F-tests in ANOVA .

For the differences between my groups, I would not use t-tests because the family-wise error rate quickly grows out of hand. To learn more about how to compare group means while controlling the familywise error rate, read my post about using post hoc tests with ANOVA . Typically, these are two-side intervals but you’d be able to use one-sided.

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November 26, 2020 at 10:51 am

Hi Jim, I had a question about the formulation of the hypotheses. When you want to test if a beta = 1 or a beta = 0. What will be the null hypotheses? I’m having trouble with finding out. Because in most cases beta = 0 is the null hypotheses but in this case you want to test if beta = 0. so i’m having my doubts can it in this case be the alternative hypotheses or is it still the null hypotheses?

Kind regards, Noa

November 27, 2020 at 1:21 am

Typically, the null hypothesis represents no effect or no relationship. As an analyst, you’re hoping that your data have enough evidence to reject the null and favor the alternative.

Assuming you’re referring to beta as in regression coefficients, zero represents no relationship. Consequently, beta = 0 is the null hypothesis.

You might hope that beta = 1, but you don’t usually include that in your alternative hypotheses. The alternative hypothesis usually states that it does not equal no effect. In other words, there is an effect but it doesn’t state what it is.

There are some exceptions to the above but I’m writing about the standard case.

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November 22, 2020 at 8:46 am

Your articles are a help to intro to econometrics students. Keep up the good work! More power to you!

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November 6, 2020 at 11:25 pm

Hello Jim. Can you help me with these please?

Write the null and alternative hypothesis using a 1-tailed and 2-tailed test for each problem. (In paragraph and symbols)

A teacher wants to know if there is a significant difference in the performance in MAT C313 between her morning and afternoon classes.

It is known that in our university canteen, the average waiting time for a customer to receive and pay for his/her order is 20 minutes. Additional personnel has been added and now the management wants to know if the average waiting time had been reduced.

November 8, 2020 at 12:29 am

I cover how to write the hypotheses for the different types of tests in this post. So, you just need to figure which type of test you need to use. In your case, you want to determine whether the mean waiting time is less than the target value of 20 minutes. That’s a 1-sample t-test because you’re comparing a mean to a target value (20 minutes). You specifically want to determine whether the mean is less than the target value. So, that’s a one-tailed test. And, you’re looking for a mean that is “less than” the target.

So, go to the one-tailed section in the post and look for the hypotheses for the effect being less than. That’s the one with the critical region on the left side of the curve.

Now, you need include your own information. In your case, you’re comparing the sample estimate to a population mean of 20. The 20 minutes is your null hypothesis value. Use the symbol mu μ to represent the population mean.

You put all that together and you get the following:

Null: μ ≥ 20 Alternative: μ 0 to denote the null hypothesis and H 1 or H A to denote the alternative hypothesis if that’s what you been using in class.

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October 17, 2020 at 12:11 pm

I was just wondering if you could please help with clarifying what the hypothesises would be for say income for gamblers and, age of gamblers. I am struggling to find which means would be compared.

October 17, 2020 at 7:05 pm

Those are both continuous variables, so you’d use either correlation or regression for them. For both of those analyses, the hypotheses are the following:

Null : The correlation or regression coefficient equals zero (i.e., there is no relationship between the variables) Alternative : The coefficient does not equal zero (i.e., there is a relationship between the variables.)

When the p-value is less than your significance level, you reject the null and conclude that a relationship exists.

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October 17, 2020 at 3:05 am

I was ask to choose and justify the reason between a one tailed and two tailed test for dummy variables, how do I do that and what does it mean?

October 17, 2020 at 7:11 pm

I don’t have enough information to answer your question. A dummy variable is also known as an indicator variable, which is a binary variable that indicates the presence or absence of a condition or characteristic. If you’re using this variable in a hypothesis test, I’d presume that you’re using a proportions test, which is based on the binomial distribution for binary data.

Choosing between a one-tailed or two-tailed test depends on subject area issues and, possibly, your research objectives. Typically, use a two-tailed test unless you have a very good reason to use a one-tailed test. To understand when you might use a one-tailed test, read my post about when to use a one-tailed hypothesis test .

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October 16, 2020 at 2:07 pm

In your one-tailed example, Minitab describes the hypotheses as “Test of mu = 100 vs > 100”. Any idea why Minitab says the null is “=” rather than “= or less than”? No ASCII character for it?

October 16, 2020 at 4:20 pm

I’m not entirely sure even though I used to work there! I know we had some discussions about how to represent that hypothesis but I don’t recall the exact reasoning. I suspect that it has to do with the conclusions that you can draw. Let’s focus on the failing to reject the null hypothesis. If the test statistic falls in that region (i.e., it is not significant), you fail to reject the null. In this case, all you know is that you have insufficient evidence to say it is different than 100. I’m pretty sure that’s why they use the equal sign because it might as well be one.

Mathematically, I think using ≤ is more accurate, which you can really see when you look at the distribution plots. That’s why I phrase the hypotheses using ≤ or ≥ as needed. However, in terms of the interpretation, the “less than” portion doesn’t really add anything of importance. You can conclude that its equal to 100 or greater than 100, but not less than 100.

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October 15, 2020 at 5:46 am

Thank you so much for your timely feedback. It helps a lot

October 14, 2020 at 10:47 am

How can i use one tailed test at 5% alpha on this problem?

A manufacturer of cellular phone batteries claims that when fully charged, the mean life of his product lasts for 26 hours with a standard deviation of 5 hours. Mr X, a regular distributor, randomly picked and tested 35 of the batteries. His test showed that the average life of his sample is 25.5 hours. Is there a significant difference between the average life of all the manufacturer’s batteries and the average battery life of his sample?

October 14, 2020 at 8:22 pm

I don’t think you’d want to use a one-tailed test. The goal is to determine whether the sample is significantly different than the manufacturer’s population average. You’re not saying significantly greater than or less than, which would be a one-tailed test. As phrased, you want a two-tailed test because it can detect a difference in either direct.

It sounds like you need to use a 1-sample t-test to test the mean. During this test, enter 26 as the test mean. The procedure will tell you if the sample mean of 25.5 hours is a significantly different from that test mean. Similarly, you’d need a one variance test to determine whether the sample standard deviation is significantly different from the test value of 5 hours.

For both of these tests, compare the p-value to your alpha of 0.05. If the p-value is less than this value, your results are statistically significant.

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September 22, 2020 at 4:16 am

Hi Jim, I didn’t get an idea that when to use two tail test and one tail test. Will you please explain?

September 22, 2020 at 10:05 pm

I have a complete article dedicated to that: When Can I Use One-Tailed Tests .

Basically, start with the assumption that you’ll use a two-tailed test but then consider scenarios where a one-tailed test can be appropriate. I talk about all of that in the article.

If you have questions after reading that, please don’t hesitate to ask!

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July 31, 2020 at 12:33 pm

Thank you so so much for this webpage.

I have two scenarios that I need some clarification. I will really appreciate it if you can take a look:

So I have several of materials that I know when they are tested after production. My hypothesis is that the earlier they are tested after production, the higher the mean value I should expect. At the same time, the later they are tested after production, the lower the mean value. Since this is more like a “greater or lesser” situation, I should use one tail. Is that the correct approach?

On the other hand, I have several mix of materials that I don’t know when they are tested after production. I only know the mean values of the test. And I only want to know whether one mean value is truly higher or lower than the other, I guess I want to know if they are only significantly different. Should I use two tail for this? If they are not significantly different, I can judge based on the mean values of test alone. And if they are significantly different, then I will need to do other type of analysis. Also, when I get my P-value for two tail, should I compare it to 0.025 or 0.05 if my confidence level is 0.05?

Thank you so much again.

July 31, 2020 at 11:19 pm

For your first, if you absolutely know that the mean must be lower the later the material is tested, that it cannot be higher, that would be a situation where you can use a one-tailed test. However, if that’s not a certainty, you’re just guessing, use a two-tail test. If you’re measuring different items at the different times, use the independent 2-sample t-test. However, if you’re measuring the same items at two time points, use the paired t-test. If it’s appropriate, using the paired t-test will give you more statistical power because it accounts for the variability between items. For more information, see my post about when it’s ok to use a one-tailed test .

For the mix of materials, use a two-tailed test because the effect truly can go either direction.

Always compare the p-value to your full significance level regardless of whether it’s a one or two-tailed test. Don’t divide the significance level in half.

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June 17, 2020 at 2:56 pm

Is it possible that we reach to opposite conclusions if we use a critical value method and p value method Secondly if we perform one tail test and use p vale method to conclude our Ho, then do we need to convert sig value of 2 tail into sig value of one tail. That can be done just by dividing it with 2

June 18, 2020 at 5:17 pm

The p-value method and critical value method will always agree as long as you’re not changing anything about how the methodology.

If you’re using statistical software, you don’t need to make any adjustments. The software will do that for you.

However, if you calculating it by hand, you’ll need to take your significance level and then look in the table for your test statistic for a one-tailed test. For example, you’ll want to look up 5% for a one-tailed test rather than a two-tailed test. That’s not as simple as dividing by two. In this article, I show examples of one-tailed and two-tailed tests for the same degrees of freedom. The t critical value for the two-tailed test is +/- 2.086 while for the one-sided test it is 1.725. It is true that probability associated with those critical values doubles for the one-tailed test (2.5% -> 5%), but the critical value itself is not half (2.086 -> 1.725). Study the first several graphs in this article to see why that is true.

For the p-value, you can take a two-tailed p-value and divide by 2 to determine the one-sided p-value. However, if you’re using statistical software, it does that for you.

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June 11, 2020 at 3:46 pm

Hello Jim, if you have the time I’d be grateful if you could shed some clarity on this scenario:

“A researcher believes that aromatherapy can relieve stress but wants to determine whether it can also enhance focus. To test this, the researcher selected a random sample of students to take an exam in which the average score in the general population is 77. Prior to the exam, these students studied individually in a small library room where a lavender scent was present. If students in this group scored significantly above the average score in general population [is this one-tailed or two-tailed hypothesis?], then this was taken as evidence that the lavender scent enhanced focus.”

Thank you for your time if you do decide to respond.

June 11, 2020 at 4:00 pm

It’s unclear from the information provided whether the researchers used a one-tailed or two-tailed test. It could be either. A two-tailed test can detect effects in both directions, so it could definitely detect an average group score above the population score. However, you could also detect that effect using a one-tailed test if it was set up correctly. So, there’s not enough information in what you provided to know for sure. It could be either.

However, that’s irrelevant to answering the question. The tricky part, as I see it, is that you’re not entirely sure about why the scores are higher. Are they higher because the lavender scent increased concentration or are they higher because the subjects have lower stress from the lavender? Or, maybe it’s not even related to the scent but some other characteristic of the room or testing conditions in which they took the test. You just know the scores are higher but not necessarily why they’re higher.

I’d say that, no, it’s not necessarily evidence that the lavender scent enhanced focus. There are competing explanations for why the scores are higher. Also, it would be best do this as an experiment with a control and treatment group where subjects are randomly assigned to either group. That process helps establish causality rather than just correlation and helps rules out competing explanations for why the scores are higher.

By the way, I spend a lot of time on these issues in my Introduction to Statistics ebook .

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June 9, 2020 at 1:47 pm

If a left tail test has an alpha value of 0.05 how will you find the value in the table

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April 19, 2020 at 10:35 am

Hi Jim, My question is in regards to the results in the table in your example of the one-sample T (Two-Tailed) test. above. What about the P-value? The P-value listed is .018. I assuming that is compared to and alpha of 0.025, correct?

In regression analysis, when I get a test statistic for the predictive variable of -2.099 and a p-value of 0.039. Am I comparing the p-value to an alpha of 0.025 or 0.05? Now if I run a Bootstrap for coefficients analysis, the results say the sig (2-tail) is 0.098. What are the critical values and alpha in this case? I’m trying to reconcile what I am seeing in both tables.

Thanks for your help.

April 20, 2020 at 3:24 am

Hi Marvalisa,

For one-tailed tests, you don’t need to divide alpha in half. If you can tell your software to perform a one-tailed test, it’ll do all the calculations necessary so you don’t need to adjust anything. So, if you’re using an alpha of 0.05 for a one-tailed test and your p-value is 0.04, it is significant. The procedures adjust the p-values automatically and it all works out. So, whether you’re using a one-tailed or two-tailed test, you always compare the p-value to the alpha with no need to adjust anything. The procedure does that for you!

The exception would be if for some reason your software doesn’t allow you to specify that you want to use a one-tailed test instead of a two-tailed test. Then, you divide the p-value from a two-tailed test in half to get the p-value for a one tailed test. You’d still compare it to your original alpha.

For regression, the same thing applies. If you want to use a one-tailed test for a cofficient, just divide the p-value in half if you can’t tell the software that you want a one-tailed test. The default is two-tailed. If your software has the option for one-tailed tests for any procedure, including regression, it’ll adjust the p-value for you. So, in the normal course of things, you won’t need to adjust anything.

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March 26, 2020 at 12:00 pm

Hey Jim, for a one-tailed hypothesis test with a .05 confidence level, should I use a 95% confidence interval or a 90% confidence interval? Thanks

March 26, 2020 at 5:05 pm

You should use a one-sided 95% confidence interval. One-sided CIs have either an upper OR lower bound but remains unbounded on the other side.

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March 16, 2020 at 4:30 pm

This is not applicable to the subject but… When performing tests of equivalence, we look at the confidence interval of the difference between two groups, and we perform two one-sided t-tests for equivalence..

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March 15, 2020 at 7:51 am

Thanks for this illustrative blogpost. I had a question on one of your points though.

By definition of H1 and H0, a two-sided alternate hypothesis is that there is a difference in means between the test and control. Not that anything is ‘better’ or ‘worse’.

Just because we observed a negative result in your example, does not mean we can conclude it’s necessarily worse, but instead just ‘different’.

Therefore while it enables us to spot the fact that there may be differences between test and control, we cannot make claims about directional effects. So I struggle to see why they actually need to be used instead of one-sided tests.

What’s your take on this?

March 16, 2020 at 3:02 am

Hi Dominic,

If you’ll notice, I carefully avoid stating better or worse because in a general sense you’re right. However, given the context of a specific experiment, you can conclude whether a negative value is better or worse. As always in statistics, you have to use your subject-area knowledge to help interpret the results. In some cases, a negative value is a bad result. In other cases, it’s not. Use your subject-area knowledge!

I’m not sure why you think that you can’t make claims about directional effects? Of course you can!

As for why you shouldn’t use one-tailed tests for most cases, read my post When Can I Use One-Tailed Tests . That should answer your questions.

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May 10, 2019 at 12:36 pm

Your website is absolutely amazing Jim, you seem like the nicest guy for doing this and I like how there’s no ulterior motive, (I wasn’t automatically signed up for emails or anything when leaving this comment). I study economics and found econometrics really difficult at first, but your website explains it so clearly its been a big asset to my studies, keep up the good work!

May 10, 2019 at 2:12 pm

Thank you so much, Jack. Your kind words mean a lot!

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April 26, 2019 at 5:05 am

Hy Jim I really need your help now pls

One-tailed and two- tailed hypothesis, is it the same or twice, half or unrelated pls

April 26, 2019 at 11:41 am

Hi Anthony,

I describe how the hypotheses are different in this post. You’ll find your answers.

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February 8, 2019 at 8:00 am

Thank you for your blog Jim, I have a Statistics exam soon and your articles let me understand a lot!

February 8, 2019 at 10:52 am

You’re very welcome! I’m happy to hear that it’s been helpful. Best of luck on your exam!

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January 12, 2019 at 7:06 am

Hi Jim, When you say target value is 5. Do you mean to say the population mean is 5 and we are trying to validate it with the help of sample mean 4.1 using Hypo tests ?.. If it is so.. How can we measure a population parameter as 5 when it is almost impossible o measure a population parameter. Please clarify

January 12, 2019 at 6:57 pm

When you set a target for a one-sample test, it’s based on a value that is important to you. It’s not a population parameter or anything like that. The example in this post uses a case where we need parts that are stronger on average than a value of 5. We derive the value of 5 by using our subject area knowledge about what is required for a situation. Given our product knowledge for the hypothetical example, we know it should be 5 or higher. So, we use that in the hypothesis test and determine whether the population mean is greater than that target value.

When you perform a one-sample test, a target value is optional. If you don’t supply a target value, you simply obtain a confidence interval for the range of values that the parameter is likely to fall within. But, sometimes there is meaningful number that you want to test for specifically.

I hope that clarifies the rational behind the target value!

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November 15, 2018 at 8:08 am

I understand that in Psychology a one tailed hypothesis is preferred. Is that so

November 15, 2018 at 11:30 am

No, there’s no overall preference for one-tailed hypothesis tests in statistics. That would be a study-by-study decision based on the types of possible effects. For more information about this decision, read my post: When Can I Use One-Tailed Tests?

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November 6, 2018 at 1:14 am

I’m grateful to you for the explanations on One tail and Two tail hypothesis test. This opens my knowledge horizon beyond what an average statistics textbook can offer. Please include more examples in future posts. Thanks

November 5, 2018 at 10:20 am

Thank you. I will search it as well.

Stan Alekman

November 4, 2018 at 8:48 pm

Jim, what is the difference between the central and non-central t-distributions w/respect to hypothesis testing?

November 5, 2018 at 10:12 am

Hi Stan, this is something I will need to look into. I know central t-distribution is the common Student t-distribution, but I don’t have experience using non-central t-distributions. There might well be a blog post in that–after I learn more!

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November 4, 2018 at 7:42 pm

this is awesome.

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Statology

Two-Tailed Hypothesis Tests: 3 Example Problems

In statistics, we use hypothesis tests to determine whether some claim about a population parameter is true or not.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter = ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter <, >, ≠ some value

There are two types of hypothesis tests:

  • One-tailed test : Alternative hypothesis contains either < or > sign
  • Two-tailed test : Alternative hypothesis contains the ≠ sign

In a two-tailed test , the alternative hypothesis always contains the not equal ( ≠ ) sign.

This indicates that we’re testing whether or not some effect exists, regardless of whether it’s a positive or negative effect.

Check out the following example problems to gain a better understanding of two-tailed tests.

Example 1: Factory Widgets

Suppose it’s assumed that the average weight of a certain widget produced at a factory is 20 grams. However, one engineer believes that a new method produces widgets that weigh less than 20 grams.

To test this, he can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

  • H 0 (Null Hypothesis): μ = 20 grams
  • H A (Alternative Hypothesis): μ ≠ 20 grams

This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal “≠” sign. The engineer believes that the new method will influence widget weight, but doesn’t specify whether it will cause average weight to increase or decrease.

To test this, he uses the new method to produce 20 widgets and obtains the following information:

  • n = 20 widgets
  • x = 19.8 grams
  • s = 3.1 grams

Plugging these values into the One Sample t-test Calculator , we obtain the following results:

  • t-test statistic: -0.288525
  • two-tailed p-value: 0.776

Since the p-value is not less than .05, the engineer fails to reject the null hypothesis.

He does not have sufficient evidence to say that the true mean weight of widgets produced by the new method is different than 20 grams.

Example 2: Plant Growth

Suppose a standard fertilizer has been shown to cause a species of plants to grow by an average of 10 inches. However, one botanist believes a new fertilizer causes this species of plants to grow by an average amount different than 10 inches.

To test this, she can perform a one-tailed hypothesis test with the following null and alternative hypotheses:

  • H 0 (Null Hypothesis): μ = 10 inches
  • H A (Alternative Hypothesis): μ ≠ 10 inches

This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal “≠” sign. The botanist believes that the new fertilizer will influence plant growth, but doesn’t specify whether it will cause average growth to increase or decrease.

To test this claim, she applies the new fertilizer to a simple random sample of 15 plants and obtains the following information:

  • n = 15 plants
  • x = 11.4 inches
  • s = 2.5 inches
  • t-test statistic: 2.1689
  • two-tailed p-value: 0.0478

Since the p-value is less than .05, the botanist rejects the null hypothesis.

She has sufficient evidence to conclude that the new fertilizer causes an average growth that is different than 10 inches.

Example 3: Studying Method

A professor believes that a certain studying technique will influence the mean score that her students receive on a certain exam, but she’s unsure if it will increase or decrease the mean score, which is currently 82.

To test this, she lets each student use the studying technique for one month leading up to the exam and then administers the same exam to each of the students.

She then performs a hypothesis test using the following hypotheses:

  • H 0 : μ = 82
  • H A : μ ≠ 82

This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal “≠” sign. The professor believes that the studying technique will influence the mean exam score, but doesn’t specify whether it will cause the mean score to increase or decrease.

To test this claim, the professor has 25 students use the new studying method and then take the exam. He collects the following data on the exam scores for this sample of students:

  • t-test statistic: 3.6586
  • two-tailed p-value: 0.0012

Since the p-value is less than .05, the professor rejects the null hypothesis.

She has sufficient evidence to conclude that the new studying method produces exam scores with an average score that is different than 82.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing What is a Directional Hypothesis? When Do You Reject the Null Hypothesis?

Featured Posts

two tailed hypothesis in research

Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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  • Indian J Crit Care Med
  • v.23(Suppl 3); 2019 Sep

An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors

Priya ranganathan.

1 Department of Anesthesiology, Critical Care and Pain, Tata Memorial Hospital, Mumbai, Maharashtra, India

2 Department of Surgical Oncology, Tata Memorial Centre, Mumbai, Maharashtra, India

The second article in this series on biostatistics covers the concepts of sample, population, research hypotheses and statistical errors.

How to cite this article

Ranganathan P, Pramesh CS. An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors. Indian J Crit Care Med 2019;23(Suppl 3):S230–S231.

Two papers quoted in this issue of the Indian Journal of Critical Care Medicine report. The results of studies aim to prove that a new intervention is better than (superior to) an existing treatment. In the ABLE study, the investigators wanted to show that transfusion of fresh red blood cells would be superior to standard-issue red cells in reducing 90-day mortality in ICU patients. 1 The PROPPR study was designed to prove that transfusion of a lower ratio of plasma and platelets to red cells would be superior to a higher ratio in decreasing 24-hour and 30-day mortality in critically ill patients. 2 These studies are known as superiority studies (as opposed to noninferiority or equivalence studies which will be discussed in a subsequent article).

SAMPLE VERSUS POPULATION

A sample represents a group of participants selected from the entire population. Since studies cannot be carried out on entire populations, researchers choose samples, which are representative of the population. This is similar to walking into a grocery store and examining a few grains of rice or wheat before purchasing an entire bag; we assume that the few grains that we select (the sample) are representative of the entire sack of grains (the population).

The results of the study are then extrapolated to generate inferences about the population. We do this using a process known as hypothesis testing. This means that the results of the study may not always be identical to the results we would expect to find in the population; i.e., there is the possibility that the study results may be erroneous.

HYPOTHESIS TESTING

A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the “alternate” hypothesis, and the opposite is called the “null” hypothesis; every study has a null hypothesis and an alternate hypothesis. For superiority studies, the alternate hypothesis states that one treatment (usually the new or experimental treatment) is superior to the other; the null hypothesis states that there is no difference between the treatments (the treatments are equal). For example, in the ABLE study, we start by stating the null hypothesis—there is no difference in mortality between groups receiving fresh RBCs and standard-issue RBCs. We then state the alternate hypothesis—There is a difference between groups receiving fresh RBCs and standard-issue RBCs. It is important to note that we have stated that the groups are different, without specifying which group will be better than the other. This is known as a two-tailed hypothesis and it allows us to test for superiority on either side (using a two-sided test). This is because, when we start a study, we are not 100% certain that the new treatment can only be better than the standard treatment—it could be worse, and if it is so, the study should pick it up as well. One tailed hypothesis and one-sided statistical testing is done for non-inferiority studies, which will be discussed in a subsequent paper in this series.

STATISTICAL ERRORS

There are two possibilities to consider when interpreting the results of a superiority study. The first possibility is that there is truly no difference between the treatments but the study finds that they are different. This is called a Type-1 error or false-positive error or alpha error. This means falsely rejecting the null hypothesis.

The second possibility is that there is a difference between the treatments and the study does not pick up this difference. This is called a Type 2 error or false-negative error or beta error. This means falsely accepting the null hypothesis.

The power of the study is the ability to detect a difference between groups and is the converse of the beta error; i.e., power = 1-beta error. Alpha and beta errors are finalized when the protocol is written and form the basis for sample size calculation for the study. In an ideal world, we would not like any error in the results of our study; however, we would need to do the study in the entire population (infinite sample size) to be able to get a 0% alpha and beta error. These two errors enable us to do studies with realistic sample sizes, with the compromise that there is a small possibility that the results may not always reflect the truth. The basis for this will be discussed in a subsequent paper in this series dealing with sample size calculation.

Conventionally, type 1 or alpha error is set at 5%. This means, that at the end of the study, if there is a difference between groups, we want to be 95% certain that this is a true difference and allow only a 5% probability that this difference has occurred by chance (false positive). Type 2 or beta error is usually set between 10% and 20%; therefore, the power of the study is 90% or 80%. This means that if there is a difference between groups, we want to be 80% (or 90%) certain that the study will detect that difference. For example, in the ABLE study, sample size was calculated with a type 1 error of 5% (two-sided) and power of 90% (type 2 error of 10%) (1).

Table 1 gives a summary of the two types of statistical errors with an example

Statistical errors

(a) Types of statistical errors
: Null hypothesis is
TrueFalse
Null hypothesis is actuallyTrueCorrect results!Falsely rejecting null hypothesis - Type I error
FalseFalsely accepting null hypothesis - Type II errorCorrect results!
(b) Possible statistical errors in the ABLE trial
There is difference in mortality between groups receiving fresh RBCs and standard-issue RBCsThere difference in mortality between groups receiving fresh RBCs and standard-issue RBCs
TruthThere is difference in mortality between groups receiving fresh RBCs and standard-issue RBCsCorrect results!Falsely rejecting null hypothesis - Type I error
There difference in mortality between groups receiving fresh RBCs and standard-issue RBCsFalsely accepting null hypothesis - Type II errorCorrect results!

In the next article in this series, we will look at the meaning and interpretation of ‘ p ’ value and confidence intervals for hypothesis testing.

Source of support: Nil

Conflict of interest: None

Two Tailed Test: Definition, Examples

Hypothesis Testing > Two Tailed Test

What is a Two Tailed Test?

two tailed test

A two tailed test tells you that you’re finding the area in the middle of a distribution. In other words, your rejection region (the place where you would reject the null hypothesis ) is in both tails.

For example, let’s say you were running a z test with an alpha level of 5% (0.05). In a one tailed test, the entire 5% would be in a single tail. But with a two tailed test, that 5% is split between the two tails, giving you 2.5% (0.025) in each tail.

Need help with a homework question? Check out our tutoring page!

Two Tailed T Test

Image: ETSU.edu

You may want to compare a sample mean to a given value of x with a t test . Let’s say your null hypothesis is that the mean is equal to 10 (μ = 10). A two tailed t test will test:

  • Is the mean greater than 10?
  • Is the mean less than 10?

If you choose an alpha level of 5%, and the f statistic is in the top 2.5% or bottom 2.5% of the probability distribution, then there is a significant difference in the means. That situation will also result in a p-value of less than 0.05. A small p-value gives you a reason to reject the null hypothesis .

Two tailed F test

To learn more watch the video below or keep reading.

two tailed hypothesis in research

Can’t see the video? Click here to watch it on YouTube.

An f test tells you if two population variances are equal. A two tailed f test is the standard type of f test which will tell you if the variances are equal or not equal. The two tailed version of test will test if one variance is greater than, or less than, the other variance. This is in comparison to the one tailed f test , which is used when you only want to test if one variance is greater than the other or that one variance is less than the other (but not both).

Everitt, B. S.; Skrondal, A. (2010), The Cambridge Dictionary of Statistics , Cambridge University Press. Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial.

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  • Knowledge Base

Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

  • State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
  • Collect data in a way designed to test the hypothesis.
  • Perform an appropriate statistical test .
  • Decide whether to reject or fail to reject your null hypothesis.
  • Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

  • H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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two tailed hypothesis in research

For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

  • an estimate of the difference in average height between the two groups.
  • a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

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The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

  • Normal distribution
  • Descriptive statistics
  • Measures of central tendency
  • Correlation coefficient

Methodology

  • Cluster sampling
  • Stratified sampling
  • Types of interviews
  • Cohort study
  • Thematic analysis

Research bias

  • Implicit bias
  • Cognitive bias
  • Survivorship bias
  • Availability heuristic
  • Nonresponse bias
  • Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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Hypothesis Testing: Upper-, Lower, and Two Tailed Tests

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The procedure for hypothesis testing is based on the ideas described above. Specifically, we set up competing hypotheses, select a random sample from the population of interest and compute summary statistics. We then determine whether the sample data supports the null or alternative hypotheses. The procedure can be broken down into the following five steps.  

  • Step 1. Set up hypotheses and select the level of significance α.

H 0 : Null hypothesis (no change, no difference);  

H 1 : Research hypothesis (investigator's belief); α =0.05

 

Upper-tailed, Lower-tailed, Two-tailed Tests

The research or alternative hypothesis can take one of three forms. An investigator might believe that the parameter has increased, decreased or changed. For example, an investigator might hypothesize:  

: μ > μ , where μ is the comparator or null value (e.g., μ =191 in our example about weight in men in 2006) and an increase is hypothesized - this type of test is called an ; : μ < μ , where a decrease is hypothesized and this is called a ; or : μ ≠ μ where a difference is hypothesized and this is called a .  

The exact form of the research hypothesis depends on the investigator's belief about the parameter of interest and whether it has possibly increased, decreased or is different from the null value. The research hypothesis is set up by the investigator before any data are collected.

 

  • Step 2. Select the appropriate test statistic.  

The test statistic is a single number that summarizes the sample information.   An example of a test statistic is the Z statistic computed as follows:

When the sample size is small, we will use t statistics (just as we did when constructing confidence intervals for small samples). As we present each scenario, alternative test statistics are provided along with conditions for their appropriate use.

  • Step 3.  Set up decision rule.  

The decision rule is a statement that tells under what circumstances to reject the null hypothesis. The decision rule is based on specific values of the test statistic (e.g., reject H 0 if Z > 1.645). The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below.

  • The decision rule depends on whether an upper-tailed, lower-tailed, or two-tailed test is proposed. In an upper-tailed test the decision rule has investigators reject H 0 if the test statistic is larger than the critical value. In a lower-tailed test the decision rule has investigators reject H 0 if the test statistic is smaller than the critical value.  In a two-tailed test the decision rule has investigators reject H 0 if the test statistic is extreme, either larger than an upper critical value or smaller than a lower critical value.
  • The exact form of the test statistic is also important in determining the decision rule. If the test statistic follows the standard normal distribution (Z), then the decision rule will be based on the standard normal distribution. If the test statistic follows the t distribution, then the decision rule will be based on the t distribution. The appropriate critical value will be selected from the t distribution again depending on the specific alternative hypothesis and the level of significance.  
  • The third factor is the level of significance. The level of significance which is selected in Step 1 (e.g., α =0.05) dictates the critical value.   For example, in an upper tailed Z test, if α =0.05 then the critical value is Z=1.645.  

The following figures illustrate the rejection regions defined by the decision rule for upper-, lower- and two-tailed Z tests with α=0.05. Notice that the rejection regions are in the upper, lower and both tails of the curves, respectively. The decision rules are written below each figure.

Rejection Region for Upper-Tailed Z Test (H : μ > μ ) with α=0.05

The decision rule is: Reject H if Z 1.645.

 

 

α

Z

0.10

1.282

0.05

1.645

0.025

1.960

0.010

2.326

0.005

2.576

0.001

3.090

0.0001

3.719

Standard normal distribution with lower tail at -1.645 and alpha=0.05

Rejection Region for Lower-Tailed Z Test (H 1 : μ < μ 0 ) with α =0.05

The decision rule is: Reject H 0 if Z < 1.645.

a

Z

0.10

-1.282

0.05

-1.645

0.025

-1.960

0.010

-2.326

0.005

-2.576

0.001

-3.090

0.0001

-3.719

Standard normal distribution with two tails

Rejection Region for Two-Tailed Z Test (H 1 : μ ≠ μ 0 ) with α =0.05

The decision rule is: Reject H 0 if Z < -1.960 or if Z > 1.960.

0.20

1.282

0.10

1.645

0.05

1.960

0.010

2.576

0.001

3.291

0.0001

3.819

The complete table of critical values of Z for upper, lower and two-tailed tests can be found in the table of Z values to the right in "Other Resources."

Critical values of t for upper, lower and two-tailed tests can be found in the table of t values in "Other Resources."

  • Step 4. Compute the test statistic.  

Here we compute the test statistic by substituting the observed sample data into the test statistic identified in Step 2.

  • Step 5. Conclusion.  

The final conclusion is made by comparing the test statistic (which is a summary of the information observed in the sample) to the decision rule. The final conclusion will be either to reject the null hypothesis (because the sample data are very unlikely if the null hypothesis is true) or not to reject the null hypothesis (because the sample data are not very unlikely).  

If the null hypothesis is rejected, then an exact significance level is computed to describe the likelihood of observing the sample data assuming that the null hypothesis is true. The exact level of significance is called the p-value and it will be less than the chosen level of significance if we reject H 0 .

Statistical computing packages provide exact p-values as part of their standard output for hypothesis tests. In fact, when using a statistical computing package, the steps outlined about can be abbreviated. The hypotheses (step 1) should always be set up in advance of any analysis and the significance criterion should also be determined (e.g., α =0.05). Statistical computing packages will produce the test statistic (usually reporting the test statistic as t) and a p-value. The investigator can then determine statistical significance using the following: If p < α then reject H 0 .  

 

 

  • Step 1. Set up hypotheses and determine level of significance

H 0 : μ = 191 H 1 : μ > 191                 α =0.05

The research hypothesis is that weights have increased, and therefore an upper tailed test is used.

  • Step 2. Select the appropriate test statistic.

Because the sample size is large (n > 30) the appropriate test statistic is

  • Step 3. Set up decision rule.  

In this example, we are performing an upper tailed test (H 1 : μ> 191), with a Z test statistic and selected α =0.05.   Reject H 0 if Z > 1.645.

We now substitute the sample data into the formula for the test statistic identified in Step 2.  

We reject H 0 because 2.38 > 1.645. We have statistically significant evidence at a =0.05, to show that the mean weight in men in 2006 is more than 191 pounds. Because we rejected the null hypothesis, we now approximate the p-value which is the likelihood of observing the sample data if the null hypothesis is true. An alternative definition of the p-value is the smallest level of significance where we can still reject H 0 . In this example, we observed Z=2.38 and for α=0.05, the critical value was 1.645. Because 2.38 exceeded 1.645 we rejected H 0 . In our conclusion we reported a statistically significant increase in mean weight at a 5% level of significance. Using the table of critical values for upper tailed tests, we can approximate the p-value. If we select α=0.025, the critical value is 1.96, and we still reject H 0 because 2.38 > 1.960. If we select α=0.010 the critical value is 2.326, and we still reject H 0 because 2.38 > 2.326. However, if we select α=0.005, the critical value is 2.576, and we cannot reject H 0 because 2.38 < 2.576. Therefore, the smallest α where we still reject H 0 is 0.010. This is the p-value. A statistical computing package would produce a more precise p-value which would be in between 0.005 and 0.010. Here we are approximating the p-value and would report p < 0.010.                  

In all tests of hypothesis, there are two types of errors that can be committed. The first is called a Type I error and refers to the situation where we incorrectly reject H 0 when in fact it is true. This is also called a false positive result (as we incorrectly conclude that the research hypothesis is true when in fact it is not). When we run a test of hypothesis and decide to reject H 0 (e.g., because the test statistic exceeds the critical value in an upper tailed test) then either we make a correct decision because the research hypothesis is true or we commit a Type I error. The different conclusions are summarized in the table below. Note that we will never know whether the null hypothesis is really true or false (i.e., we will never know which row of the following table reflects reality).

Table - Conclusions in Test of Hypothesis

 

is True

Correct Decision

Type I Error

is False

Type II Error

Correct Decision

In the first step of the hypothesis test, we select a level of significance, α, and α= P(Type I error). Because we purposely select a small value for α, we control the probability of committing a Type I error. For example, if we select α=0.05, and our test tells us to reject H 0 , then there is a 5% probability that we commit a Type I error. Most investigators are very comfortable with this and are confident when rejecting H 0 that the research hypothesis is true (as it is the more likely scenario when we reject H 0 ).

When we run a test of hypothesis and decide not to reject H 0 (e.g., because the test statistic is below the critical value in an upper tailed test) then either we make a correct decision because the null hypothesis is true or we commit a Type II error. Beta (β) represents the probability of a Type II error and is defined as follows: β=P(Type II error) = P(Do not Reject H 0 | H 0 is false). Unfortunately, we cannot choose β to be small (e.g., 0.05) to control the probability of committing a Type II error because β depends on several factors including the sample size, α, and the research hypothesis. When we do not reject H 0 , it may be very likely that we are committing a Type II error (i.e., failing to reject H 0 when in fact it is false). Therefore, when tests are run and the null hypothesis is not rejected we often make a weak concluding statement allowing for the possibility that we might be committing a Type II error. If we do not reject H 0 , we conclude that we do not have significant evidence to show that H 1 is true. We do not conclude that H 0 is true.

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 The most common reason for a Type II error is a small sample size.

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What Is a Two-Tailed Test?

Understanding a two-tailed test, special considerations, two-tailed vs. one-tailed test.

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What Is a Two-Tailed Test? Definition and Example

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two tailed hypothesis in research

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A two-tailed test, in statistics, is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater than or less than a certain range of values. It is used in null-hypothesis testing and testing for statistical significance . If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.

Key Takeaways

  • In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values.
  • It is used in null-hypothesis testing and testing for statistical significance.
  • If the sample being tested falls into either of the critical areas, the alternative hypothesis is accepted instead of the null hypothesis.
  • By convention two-tailed tests are used to determine significance at the 5% level, meaning each side of the distribution is cut at 2.5%.

A basic concept of inferential statistics is hypothesis testing , which determines whether a claim is true or not given a population parameter. A hypothesis test that is designed to show whether the mean of a sample is significantly greater than and significantly less than the mean of a population is referred to as a two-tailed test. The two-tailed test gets its name from testing the area under both tails of a normal distribution , although the test can be used in other non-normal distributions.

A two-tailed test is designed to examine both sides of a specified data range as designated by the probability distribution involved. The probability distribution should represent the likelihood of a specified outcome based on predetermined standards. This requires the setting of a limit designating the highest (or upper) and lowest (or lower) accepted variable values included within the range. Any data point that exists above the upper limit or below the lower limit is considered out of the acceptance range and in an area referred to as the rejection range.

There is no inherent standard about the number of data points that must exist within the acceptance range. In instances where precision is required, such as in the creation of pharmaceutical drugs, a rejection rate of 0.001% or less may be instituted. In instances where precision is less critical, such as the number of food items in a product bag, a rejection rate of 5% may be appropriate.

A two-tailed test can also be used practically during certain production activities in a firm, such as with the production and packaging of candy at a particular facility. If the production facility designates 50 candies per bag as its goal, with an acceptable distribution of 45 to 55 candies, any bag found with an amount below 45 or above 55 is considered within the rejection range.

To confirm the packaging mechanisms are properly calibrated to meet the expected output, random sampling may be taken to confirm accuracy. A simple random sample takes a small, random portion of the entire population to represent the entire data set, where each member has an equal probability of being chosen.

For the packaging mechanisms to be considered accurate, an average of 50 candies per bag with an appropriate distribution is desired. Additionally, the number of bags that fall within the rejection range needs to fall within the probability distribution limit considered acceptable as an error rate. Here, the null hypothesis would be that the mean is 50 while the alternate hypothesis would be that it is not 50.

If, after conducting the two-tailed test, the z-score falls in the rejection region, meaning that the deviation is too far from the desired mean, then adjustments to the facility or associated equipment may be required to correct the error. Regular use of two-tailed testing methods can help ensure production stays within limits over the long term.

Be careful to note if a statistical test is one- or two-tailed as this will greatly influence a model's interpretation.

When a hypothesis test is set up to show that the sample mean would be only higher than the population mean, this is referred to as a  one-tailed test . A formulation of this hypothesis would be, for example, that "the returns on an investment fund would be  at least  x%." One-tailed tests could also be set up to show that the sample mean could be only less than the population mean. The key difference from a two-tailed test is that in a two-tailed test, the sample mean could be different from the population mean by being  either  higher or lower than it.

If the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis. A one-tailed test is also known as a directional hypothesis or directional test.

A two-tailed test, on the other hand, is designed to examine both sides of a specified data range to test whether a sample is greater than or less than the range of values.

Example of a Two-Tailed Test

As a hypothetical example, imagine that a new  stockbroker , named XYZ, claims that their brokerage fees are lower than that of your current stockbroker, ABC) Data available from an independent research firm indicates that the mean and standard deviation of all ABC broker clients are $18 and $6, respectively.

A sample of 100 clients of ABC is taken, and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and the sample standard deviation is $6, can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?

  • H 0 : Null Hypothesis: mean = 18
  • H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)
  • Rejection region: Z <= - Z 2.5  and Z>=Z 2.5  (assuming 5% significance level, split 2.5 each on either side).
  • Z = (sample mean – mean) / (std-dev / sqrt (no. of samples)) = (18.75 – 18) / (6/(sqrt(100)) = 1.25

This calculated Z value falls between the two limits defined by: - Z 2.5  = -1.96 and Z 2.5  = 1.96.

This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker. Therefore, the null hypothesis cannot be rejected. Alternatively, the p-value = P(Z< -1.25)+P(Z >1.25) = 2 * 0.1056 = 0.2112 = 21.12%, which is greater than 0.05 or 5%, leads to the same conclusion.

How Is a Two-Tailed Test Designed?

A two-tailed test is designed to determine whether a claim is true or not given a population parameter. It examines both sides of a specified data range as designated by the probability distribution involved. As such, the probability distribution should represent the likelihood of a specified outcome based on predetermined standards.

What Is the Difference Between a Two-Tailed and One-Tailed Test?

A two-tailed hypothesis test is designed to show whether the sample mean is significantly greater than  or  significantly less than the mean of a population. The two-tailed test gets its name from testing the area under both tails (sides) of a normal distribution. A one-tailed hypothesis test, on the other hand, is set up to show only one test; that the sample mean would be higher than the population mean, or, in a separate test, that the sample mean would be lower than the population mean.

What Is a Z-score?

A Z-score numerically describes a value's relationship to the mean of a group of values and is measured in terms of the number of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score whereas Z-scores of 1.0 and -1.0 would indicate values one standard deviation above or below the mean. In most large data sets, 99% of values have a Z-score between -3 and 3, meaning they lie within three standard deviations above and below the mean.

San Jose State University. " 6: Introduction to Null Hypothesis Significance Testing ."

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Research Hypothesis In Psychology: Types, & Examples

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A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

  • A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
  • It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
  • A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
  • Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
  • For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
  • Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.
Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

  • Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

hypothesis

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.
  • Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
  • However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

  • Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
  • Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
  • Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
  • Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
  • Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

  • The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
  • The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

  • Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
  • Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
  • Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
  • Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
  • Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
  • Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
  • Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
  • Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

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4 One-tailed vs two-tailed test

To gain a deeper understanding of how to conduct a hypothesis test, this section will delve into the concepts of one-tailed and two-tailed tests. These tests are vital tools in statistical hypothesis testing, and the decision of which test to employ depends on the research question and hypothesis under examination. It is crucial to give careful thought to the suitable type of test to ensure that the hypothesis is thoroughly tested and precise conclusions are derived from the data. This section will elaborate on this topic in greater detail.

To commence, complete the following activity pertaining to the formulation of null and alternative hypotheses. This exercise may be somewhat challenging, but it serves as an excellent introduction to upcoming discussions – don’t be concerned if you find it difficult!

Activity 3 Hypotheses setting

Read the following statements and then develop a null hypothesis and an alternative hypothesis.

‘It is believed that OU students need to set aside no longer than, on average, 15 hours to study an entire session of an OU course. However, a researcher believes that OU students spend longer studying an entire session of an OU course.’

H 0 : OU students spend, on average, no more than 15 hours studying an entire session of OU course.

H a : OU students spend, on average, more than 15 hours studying an entire session of OU course.

They can also be written as:

H 0 : µ ≤ 15 hours studies

H a : µ > 15 hours studies

µ is a symbol for a population mean. Remember, H 0 and H a are always opposites.

Did you identify any differences between the hypotheses you developed in Activity 1 and Activity 3? The set of hypotheses in Activity 1 has an equal (=) or not equal (≠) supposition (sign) in the statement. However, in Activity 3, the set of hypotheses has less than or equal to (≤) and greater than (>) supposition (sign) in the statement. This creates different conditions that lead to acceptance or rejection of the null hypothesis.

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Statistical Methods and Data Analytics

FAQ: What are the differences between one-tailed and two-tailed tests?

When you conduct a test of statistical significance, whether it is from a correlation, an ANOVA, a regression or some other kind of test, you are given a p-value somewhere in the output.  If your test statistic is symmetrically distributed, you can select one of three alternative hypotheses. Two of these correspond to one-tailed tests and one corresponds to a two-tailed test.  However, the p-value presented is (almost always) for a two-tailed test.  But how do you choose which test?  Is the p-value appropriate for your test? And, if it is not, how can you calculate the correct p-value for your test given the p-value in your output?  

What is a two-tailed test?

First let’s start with the meaning of a two-tailed test.  If you are using a significance level of 0.05, a two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction.  This means that .025 is in each tail of the distribution of your test statistic. When using a two-tailed test, regardless of the direction of the relationship you hypothesize, you are testing for the possibility of the relationship in both directions.  For example, we may wish to compare the mean of a sample to a given value x using a t-test.  Our null hypothesis is that the mean is equal to x . A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x . The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.     

What is a one-tailed test?

Next, let’s discuss the meaning of a one-tailed test.  If you are using a significance level of .05, a one-tailed test allots all of your alpha to testing the statistical significance in the one direction of interest.  This means that .05 is in one tail of the distribution of your test statistic. When using a one-tailed test, you are testing for the possibility of the relationship in one direction and completely disregarding the possibility of a relationship in the other direction.  Let’s return to our example comparing the mean of a sample to a given value x using a t-test.  Our null hypothesis is that the mean is equal to x . A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x , but not both. Then, depending on the chosen tail, the mean is significantly greater than or less than x if the test statistic is in the top 5% of its probability distribution or bottom 5% of its probability distribution, resulting in a p-value less than 0.05.  The one-tailed test provides more power to detect an effect in one direction by not testing the effect in the other direction. A discussion of when this is an appropriate option follows.   

When is a one-tailed test appropriate?

Because the one-tailed test provides more power to detect an effect, you may be tempted to use a one-tailed test whenever you have a hypothesis about the direction of an effect. Before doing so, consider the consequences of missing an effect in the other direction.  Imagine you have developed a new drug that you believe is an improvement over an existing drug.  You wish to maximize your ability to detect the improvement, so you opt for a one-tailed test. In doing so, you fail to test for the possibility that the new drug is less effective than the existing drug.  The consequences in this example are extreme, but they illustrate a danger of inappropriate use of a one-tailed test.

So when is a one-tailed test appropriate? If you consider the consequences of missing an effect in the untested direction and conclude that they are negligible and in no way irresponsible or unethical, then you can proceed with a one-tailed test. For example, imagine again that you have developed a new drug. It is cheaper than the existing drug and, you believe, no less effective.  In testing this drug, you are only interested in testing if it less effective than the existing drug.  You do not care if it is significantly more effective.  You only wish to show that it is not less effective. In this scenario, a one-tailed test would be appropriate. 

When is a one-tailed test NOT appropriate?

Choosing a one-tailed test for the sole purpose of attaining significance is not appropriate.  Choosing a one-tailed test after running a two-tailed test that failed to reject the null hypothesis is not appropriate, no matter how "close" to significant the two-tailed test was.  Using statistical tests inappropriately can lead to invalid results that are not replicable and highly questionable–a steep price to pay for a significance star in your results table!   

Deriving a one-tailed test from two-tailed output

The default among statistical packages performing tests is to report two-tailed p-values.  Because the most commonly used test statistic distributions (standard normal, Student’s t) are symmetric about zero, most one-tailed p-values can be derived from the two-tailed p-values.   

Below, we have the output from a two-sample t-test in Stata.  The test is comparing the mean male score to the mean female score.  The null hypothesis is that the difference in means is zero.  The two-sided alternative is that the difference in means is not zero.  There are two one-sided alternatives that one could opt to test instead: that the male score is higher than the female score (diff  > 0) or that the female score is higher than the male score (diff < 0).  In this instance, Stata presents results for all three alternatives.  Under the headings Ha: diff < 0 and Ha: diff > 0 are the results for the one-tailed tests. In the middle, under the heading Ha: diff != 0 (which means that the difference is not equal to 0), are the results for the two-tailed test. 

Two-sample t test with equal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- male | 91 50.12088 1.080274 10.30516 47.97473 52.26703 female | 109 54.99083 .7790686 8.133715 53.44658 56.53507 ---------+-------------------------------------------------------------------- combined | 200 52.775 .6702372 9.478586 51.45332 54.09668 ---------+-------------------------------------------------------------------- diff | -4.869947 1.304191 -7.441835 -2.298059 ------------------------------------------------------------------------------ Degrees of freedom: 198 Ho: mean(male) - mean(female) = diff = 0 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 t = -3.7341 t = -3.7341 t = -3.7341 P < t = 0.0001 P > |t| = 0.0002 P > t = 0.9999

Note that the test statistic, -3.7341, is the same for all of these tests.  The two-tailed p-value is P > |t|. This can be rewritten as P(>3.7341) + P(< -3.7341).  Because the t-distribution is symmetric about zero, these two probabilities are equal: P > |t| = 2 *  P(< -3.7341).  Thus, we can see that the two-tailed p-value is twice the one-tailed p-value for the alternative hypothesis that (diff < 0).  The other one-tailed alternative hypothesis has a p-value of P(>-3.7341) = 1-(P<-3.7341) = 1-0.0001 = 0.9999.   So, depending on the direction of the one-tailed hypothesis, its p-value is either 0.5*(two-tailed p-value) or 1-0.5*(two-tailed p-value) if the test statistic symmetrically distributed about zero. 

In this example, the two-tailed p-value suggests rejecting the null hypothesis of no difference. Had we opted for the one-tailed test of (diff > 0), we would fail to reject the null because of our choice of tails. 

The output below is from a regression analysis in Stata.  Unlike the example above, only the two-sided p-values are presented in this output.

Source | SS df MS Number of obs = 200 -------------+------------------------------ F( 2, 197) = 46.58 Model | 7363.62077 2 3681.81039 Prob > F = 0.0000 Residual | 15572.5742 197 79.0486001 R-squared = 0.3210 -------------+------------------------------ Adj R-squared = 0.3142 Total | 22936.195 199 115.257261 Root MSE = 8.8909 ------------------------------------------------------------------------------ socst | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- science | .2191144 .0820323 2.67 0.008 .0573403 .3808885 math | .4778911 .0866945 5.51 0.000 .3069228 .6488594 _cons | 15.88534 3.850786 4.13 0.000 8.291287 23.47939 ------------------------------------------------------------------------------

For each regression coefficient, the tested null hypothesis is that the coefficient is equal to zero.  Thus, the one-tailed alternatives are that the coefficient is greater than zero and that the coefficient is less than zero. To get the p-value for the one-tailed test of the variable science having a coefficient greater than zero, you would divide the .008 by 2, yielding .004 because the effect is going in the predicted direction. This is P(>2.67). If you had made your prediction in the other direction (the opposite direction of the model effect), the p-value would have been 1 – .004 = .996.  This is P(<2.67). For all three p-values, the test statistic is 2.67. 

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Examples

Research Question and Hypothesis

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two tailed hypothesis in research

Navigating the intricacies of research begins with crafting well-defined research questions and hypothesis statements. These essential components guide the entire research process, shaping investigations and analyses. In this comprehensive guide, explore the art of formulating research questions and hypothesis statements. Learn how to create focused, inquiry-driven questions and construct research hypothesis statements that capture the essence of your study. Unveil examples and invaluable tips to enhance your research endeavors.

What is an example of a Research Question and Hypothesis Statement?

Research Question: How does regular exercise impact the mental well-being of college students?

Hypothesis Statement: College students who engage in regular exercise experience improved mental well-being compared to those who do not exercise regularly.

In this example, the research question focuses on the relationship between exercise and mental well-being among college students. The hypothesis statement predicts a specific outcome, stating that there will be a positive impact on mental well-being for those who exercise regularly. The hypothesis guides the research process and provides a clear expectation for the study’s results.

100 Research Question and Hypothesis Statement Examples

Research Question and Hypothesis Statement Examples

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Education How does the integration of technology impact student engagement in elementary classrooms? Elementary students exposed to technology-enhanced lessons exhibit higher levels of engagement.
Health What is the relationship between sleep quality and stress levels among working professionals? Working professionals who experience higher sleep quality report lower levels of stress.
Environment How does exposure to urban green spaces influence residents’ mental well-being? Residents with regular access to urban green spaces exhibit higher levels of mental well-being.
Economics What impact does minimum wage increase have on small business profitability? Small businesses in regions with minimum wage increases experience decreased profitability.
Social Media How do social media influencers affect consumer purchasing decisions? Consumers are more likely to make decisions based on recommendations from social media influencers.
Gender Studies What is the perception of gender roles among adolescents in a multicultural society? Adolescents in multicultural societies have fluid perceptions of traditional gender roles.
Nutrition Is there a correlation between diet quality and academic performance among college students? College students with healthier diets show better academic performance.
Political Science How does media framing influence public opinion on climate change policies? Media framing significantly impacts public opinion on climate change policies.
Criminal Justice What factors contribute to recidivism rates among juvenile offenders? Juvenile offenders with strong support systems are less likely to engage in recidivism.
Cultural Studies How does exposure to diverse cultural experiences impact cultural sensitivity among students? Students engaging in diverse cultural experiences develop higher cultural sensitivity.
Technology Adoption What factors influence the adoption of e-commerce platforms among older adults? Older adults with higher digital literacy levels are more likely to adopt e-commerce platforms.
Language Acquisition How does bilingualism impact cognitive development in children? Bilingual children exhibit enhanced cognitive flexibility and problem-solving skills.
Urban Planning What are the effects of green infrastructure on urban heat island mitigation? Urban areas with green infrastructure experience lower temperatures during heatwaves.
Parenting Styles What role does authoritative parenting play in adolescent self-esteem development? Adolescents raised by authoritative parents tend to have higher self-esteem levels.
Workplace Diversity How does workplace diversity impact employee satisfaction and job performance? Diverse workforces lead to higher employee satisfaction and improved job performance.
Cultural Influence on Perception How do cultural backgrounds affect individuals’ perception of facial expressions? Cultural backgrounds influence how individuals interpret facial expressions.
Music and Mood Does listening to music of different genres have varying effects on mood regulation? Different music genres evoke distinct emotional responses, influencing mood regulation.
Advertising Effectiveness What factors contribute to the effectiveness of online banner advertisements? Personalized online banner ads with compelling visuals are more effective in user engagement.
Relationship Satisfaction How does communication style affect relationship satisfaction among couples? Open and empathetic communication leads to higher relationship satisfaction among couples.
Cultural Identity and Mental Health How does the integration of cultural identity influence mental health outcomes among immigrants? Immigrant adolescents who maintain cultural identity tend to exhibit better mental health.
Education How does the integration of technology impact student engagement in elementary classrooms? Elementary students exposed to technology-enhanced lessons exhibit higher levels of engagement.
Health What is the relationship between sleep quality and stress levels among working professionals? Working professionals who experience higher sleep quality report lower levels of stress.
Environment How does exposure to urban green spaces influence residents’ mental well-being? Residents with regular access to urban green spaces exhibit higher levels of mental well-being.
Economics What impact does minimum wage increase have on small business profitability? Small businesses in regions with minimum wage increases experience decreased profitability.
Social Media How do social media influencers affect consumer purchasing decisions? Consumers are more likely to make decisions based on recommendations from social media influencers.
Gender Studies What is the perception of gender roles among adolescents in a multicultural society? Adolescents in multicultural societies have fluid perceptions of traditional gender roles.
Nutrition Is there a correlation between diet quality and academic performance among college students? College students with healthier diets show better academic performance.
Political Science How does media framing influence public opinion on climate change policies? Media framing significantly impacts public opinion on climate change policies.
Criminal Justice What factors contribute to recidivism rates among juvenile offenders? Juvenile offenders with strong support systems are less likely to engage in recidivism.
Cultural Studies How does exposure to diverse cultural experiences impact cultural sensitivity among students? Students engaging in diverse cultural experiences develop higher cultural sensitivity.
Technology Adoption What factors influence the adoption of e-commerce platforms among older adults? Older adults with higher digital literacy levels are more likely to adopt e-commerce platforms.
Language Acquisition How does bilingualism impact cognitive development in children? Bilingual children exhibit enhanced cognitive flexibility and problem-solving skills.
Urban Planning What are the effects of green infrastructure on urban heat island mitigation? Urban areas with green infrastructure experience lower temperatures during heatwaves.
Parenting Styles What role does authoritative parenting play in adolescent self-esteem development? Adolescents raised by authoritative parents tend to have higher self-esteem levels.
Workplace Diversity How does workplace diversity impact employee satisfaction and job performance? Diverse workforces lead to higher employee satisfaction and improved job performance.
Cultural Influence on Perception How do cultural backgrounds affect individuals’ perception of facial expressions? Cultural backgrounds influence how individuals interpret facial expressions.
Music and Mood Does listening to music of different genres have varying effects on mood regulation? Different music genres evoke distinct emotional responses, influencing mood regulation.
Advertising Effectiveness What factors contribute to the effectiveness of online banner advertisements? Personalized online banner ads with compelling visuals are more effective in user engagement.
Relationship Satisfaction How does communication style affect relationship satisfaction among couples? Open and empathetic communication leads to higher relationship satisfaction among couples.
Cultural Identity and Mental Health How does the integration of cultural identity influence mental health outcomes among immigrants? Immigrant adolescents who maintain cultural identity tend to exhibit better mental health.
Educational Psychology How does feedback delivery method affect students’ motivation in online learning environments? Students receiving personalized feedback in online courses show higher motivation levels.
Healthcare Access What factors influence individuals’ access to quality healthcare services in rural areas? Rural residents with reliable transportation options have better access to quality healthcare.
Environmental Impact How does deforestation impact biodiversity in tropical rainforests? Increased rates of deforestation lead to a decline in biodiversity within tropical rainforests.
Consumer Behavior What role do product reviews play in consumers’ purchasing decisions on e-commerce platforms? Consumers are more likely to choose products with positive reviews when shopping online.
Language Perception How does language fluency affect individuals’ perception of different accents? Individuals fluent in a language are more likely to accurately differentiate between accents.
Food Preferences What factors contribute to the preference for spicy foods among certain cultural groups? Cultural background significantly influences the preference for spicy foods among individuals.
Urban Mobility How does the availability of public transportation impact car usage in urban areas? Cities with efficient public transportation systems experience reduced car usage by residents.
Political Engagement What factors determine young adults’ engagement in political activities? Young adults with higher levels of education tend to be more engaged in political activities.
Artificial Intelligence in Finance How does the integration of AI-based algorithms impact stock trading accuracy? AI algorithms improve stock trading accuracy when integrated into financial trading systems.
Body Image Perception How does exposure to idealized body images in media influence individuals’ self-perception? Individuals exposed to idealized body images in media tend to have lower self-esteem levels.
Technology Adoption How does user interface design impact the adoption rate of mobile applications? Mobile applications with intuitive user interfaces are more likely to have higher adoption rates.
Cultural Influence on Education How does cultural background affect students’ learning preferences and styles? Students from different cultural backgrounds have varied learning preferences and styles.
Economic Development What role does foreign direct investment play in the economic growth of developing countries? Developing countries with higher foreign direct investment experience greater economic growth.
Social Interaction in Virtual Reality How does virtual reality impact social interaction and communication among users? Users of virtual reality platforms tend to experience enhanced social interaction and communication.
Body-Mind Connection What is the relationship between physical exercise and cognitive functioning in elderly adults? Elderly adults who engage in regular physical exercise exhibit better cognitive functioning.
Political Polarization How does exposure to partisan media influence individuals’ political views? Exposure to partisan media significantly shapes and reinforces individuals’ political views.
Work-Life Balance What factors contribute to employees’ perception of work-life balance in corporate settings? Employees with flexible work arrangements tend to perceive better work-life balance.
Genetic Influence on Behavior To what extent does genetic predisposition influence risk-taking behavior in individuals? Individuals with a genetic predisposition to risk-taking behavior are more likely to exhibit such behavior.
Media Representation of Gender How are gender roles and stereotypes portrayed in children’s animated television shows? Children’s animated television shows often perpetuate traditional gender roles and stereotypes.
Economic Inequality What is the relationship between income inequality and social mobility in urban areas? Urban areas with higher income inequality tend to have lower social mobility rates.
Nutrition and Cognitive Function How does dietary intake influence cognitive function in school-aged children? School-aged children with balanced diets tend to exhibit better cognitive function.
Technology Addiction How does excessive smartphone usage impact individuals’ overall well-being? Excessive smartphone usage is negatively correlated with individuals’ overall well-being.
Creativity and Age How does age influence individuals’ creativity and innovation levels? Creativity and innovation levels tend to decrease with advancing age.
Online Learning Effectiveness What factors determine the effectiveness of online learning compared to traditional classroom learning? Online learning is equally effective as traditional classroom learning in academic outcomes.
Media Exposure and Body Image How does exposure to digitally altered images in media impact body image dissatisfaction among adolescents? Adolescents exposed to digitally altered images in media are more likely to experience body image dissatisfaction.
Motivation in the Workplace How does recognition and rewards affect employees’ motivation in the workplace? Employees who receive regular recognition and rewards tend to exhibit higher levels of motivation.
Social Media and Mental Health What is the relationship between social media usage and mental health among adolescents? Adolescents who spend excessive time on social media platforms tend to experience poorer mental health.
Artistic Expression and Emotion How does artistic expression influence emotional expression and regulation in individuals? Individuals engaged in artistic activities tend to have enhanced emotional expression and regulation.
Cultural Diversity in Education How does a diverse teaching staff impact students’ cultural awareness and understanding? Schools with a diverse teaching staff promote greater cultural awareness and understanding among students.
Economic Impact of Tourism What is the economic impact of tourism on local communities and businesses? Tourism significantly contributes to the economic growth of local communities and businesses.
Social Media and Self-Esteem How does social media usage impact adolescents’ self-esteem and body image? Adolescents who spend more time on social media platforms are more likely to experience lower self-esteem and body image issues.
Gender Wage Gap What factors contribute to the gender wage gap in the corporate sector? Gender wage gaps in the corporate sector can be attributed to disparities in job roles, negotiation skills, and workplace biases.
Influence of Parenting Styles How do different parenting styles influence adolescents’ academic achievement? Adolescents raised in authoritative parenting environments tend to achieve higher academic success compared to other styles.
Peer Pressure and Risk Behavior How does peer pressure influence risk behaviors among teenagers? Teenagers who succumb to peer pressure are more likely to engage in risky behaviors, such as substance abuse and delinquency.
Media Exposure and Violence Is there a link between exposure to violent media and aggressive behavior in children? Children exposed to violent media content are more likely to exhibit aggressive behaviors in real-life situations.
Advertising Appeals How do emotional appeals versus rational appeals influence consumer purchasing decisions? Consumers are more likely to make emotional purchasing decisions when exposed to emotional advertising appeals.
Work-Related Stress and Health How does work-related stress impact employees’ physical and mental health? Employees experiencing high levels of work-related stress are more prone to physical and mental health issues.
Social Support and Mental Health What role does social support play in promoting positive mental health outcomes? Individuals with strong social support networks tend to exhibit better mental health outcomes and coping mechanisms.
Impact of Music on Memory Can listening to music improve memory recall in learning environments? Background music with a moderate tempo and melody can enhance memory recall in learning environments.
Urbanization and Air Quality How does rapid urbanization affect air quality in metropolitan areas? Rapid urbanization is associated with deteriorating air quality due to increased pollution levels in metropolitan areas.
Impact of Social Media on Relationships How does frequent social media use influence the quality of romantic relationships among young adults? Young adults who spend more time on social media tend to have lower relationship satisfaction and communication.
Cultural Diversity and Workplace What is the impact of cultural diversity on workplace productivity and collaboration? Workplaces that embrace cultural diversity experience increased productivity and better collaboration among employees.
Technology and Academic Performance How does the use of digital devices affect students’ academic performance in classrooms? Students who use digital devices excessively during classes tend to have lower academic performance compared to those who limit usage.
Influence of Family Structure How does family structure influence adolescents’ emotional development and well-being? Adolescents from single-parent households exhibit higher levels of emotional distress compared to those from two-parent households.
Personality Traits and Leadership What personality traits contribute to effective leadership in various organizational contexts? Leaders with high levels of extroversion, emotional intelligence, and adaptability tend to be more effective in guiding teams and organizations.
Exercise and Mental Health Does regular exercise have a positive impact on individuals’ mental health and well-being? Regular physical exercise is associated with improved mental health outcomes and reduced symptoms of anxiety and depression.
Social Media and Political Engagement How does social media usage influence individuals’ participation in political discussions and activities? Individuals who engage in political discussions on social media are more likely to actively participate in offline political activities.
Stress and Sleep Quality How does chronic stress affect sleep quality and patterns in adults? Adults experiencing chronic stress tend to have disrupted sleep patterns and lower sleep quality compared to those with lower stress levels.
Role of Nutrition in Aging What role does nutrition play in slowing down the aging process and promoting healthy aging? Individuals who consume a diet rich in antioxidants and nutrients tend to experience slower aging and better overall health in older age.
Gender Stereotypes in STEM Fields How do gender stereotypes influence individuals’ career choices in STEM fields (science, technology, engineering, mathematics)? Gender stereotypes contribute to the underrepresentation of women in STEM fields by discouraging their pursuit of STEM careers.
Social Media and Body Image What is the relationship between social media usage and body dissatisfaction among adolescents? Adolescents who spend more time on social media platforms are more likely to experience negative body image and dissatisfaction.
Impact of Arts Education on Creativity How does participation in arts education programs influence students’ creative thinking skills? Students who engage in arts education programs tend to exhibit enhanced creative thinking skills compared to those who do not.
Urban Green Spaces and Mental Health How do urban green spaces impact individuals’ mental health and well-being? Access to urban green spaces is positively correlated with improved mental health outcomes and reduced stress levels among urban residents.
Technology Use and Academic Achievement How does the amount of time spent on digital devices impact students’ academic achievement? Students who excessively use digital devices for non-academic purposes tend to have lower academic achievement compared to those who limit usage.
Impact of Social Support on Recovery Does having a strong social support system aid in the recovery process after major surgeries? Patients with robust social support networks tend to experience faster recovery and better postoperative outcomes following major surgeries.
Impact of Parental Involvement in Education How does parental involvement affect students’ academic performance and motivation? Students with actively involved parents tend to have higher academic performance and greater motivation in school.
Influence of Peer Feedback on Learning Does receiving peer feedback enhance students’ learning outcomes in collaborative projects? Students who receive constructive peer feedback during collaborative projects show improved learning outcomes.
Music and Stress Reduction Can listening to music help reduce stress levels in high-stress work environments? Employees who listen to soothing music during work breaks experience reduced stress and increased relaxation.
Effects of Sleep on Memory How does sleep duration impact memory consolidation and recall in college students? College students with sufficient sleep duration tend to exhibit better memory consolidation and recall abilities.
Cultural Sensitivity in Healthcare How does cultural sensitivity training impact healthcare providers’ patient communication? Healthcare providers who undergo cultural sensitivity training exhibit improved patient communication and trust.
Impact of Outdoor Play on Child Development Does outdoor play contribute to better motor skills and cognitive development in young children? Young children who engage in outdoor play activities demonstrate improved motor skills and cognitive development.
Relationship Between Diet and Heart Health What is the connection between dietary habits and the risk of cardiovascular diseases? Individuals with a diet high in saturated fats and sodium have an increased risk of cardiovascular diseases.
Impact of Classroom Design on Learning How does classroom design influence students’ engagement and learning outcomes in schools? Classroom designs with flexible seating and interactive elements foster increased student engagement and learning.
Technology Use and Family Communication How does technology use affect family communication patterns and relationships? Families that excessively rely on technology for communication experience reduced quality in family relationships.
Motivation and Employee Productivity How does intrinsic motivation impact employee productivity in the workplace? Employees who are intrinsically motivated tend to exhibit higher levels of productivity in their work tasks.
Impact of Nutrition on Cognitive Function Can a balanced diet improve cognitive function and concentration in older adults? Older adults with a balanced diet rich in antioxidants and nutrients tend to experience improved cognitive function.
Factors Affecting Online Shopping Behavior What factors influence consumers’ decision-making in online shopping? Consumers’ online shopping behavior is influenced by factors such as price, reviews, convenience, and website design.
Effectiveness of Online Learning Platforms How effective are online learning platforms in enhancing students’ knowledge retention and engagement? Students who use interactive online learning platforms show higher levels of knowledge retention and engagement.
Media Exposure and Political Beliefs Does media exposure shape individuals’ political beliefs and opinions? Individuals exposed to polarized media content tend to develop more extreme political beliefs and opinions.
Impact of Meditation on Stress Reduction How does regular meditation practice contribute to stress reduction and mental well-being? Regular meditation practice is associated with decreased stress levels and improved mental well-being in individuals.
Social Media Influencer Marketing What is the impact of social media influencer marketing on consumer purchasing decisions? Consumers influenced by social media influencers are more likely to make purchasing decisions based on their recommendations.
Factors Influencing Job Satisfaction What factors contribute to employees’ job satisfaction in the workplace? Employees’ job satisfaction is influenced by factors such as work-life balance, compensation, recognition, and job security.
Impact of Early Childhood Education How does early childhood education affect cognitive development and school readiness? Children who receive quality early childhood education tend to demonstrate enhanced cognitive development and school readiness.
Effects of Exercise on Mental Health Can regular physical exercise improve mental health and reduce symptoms of anxiety and depression? Individuals who engage in regular exercise experience improved mental health outcomes and reduced symptoms of anxiety and depression.
Impact of Social Media on Self-Esteem Does excessive social media use contribute to lower self-esteem levels among adolescents? Adolescents who spend more time on social media platforms tend to have lower self-esteem compared to those who limit usage.
Effects of Video Games on Aggression What is the relationship between violent video game exposure and aggressive behavior in adolescents? Adolescents exposed to violent video games are more likely to exhibit aggressive behavior compared to those who are not exposed.
Impact of Gender Diversity on Team Performance How does gender diversity influence team performance in corporate settings? Teams with diverse gender compositions tend to achieve higher levels of performance compared to less diverse teams.
Effect of Music Tempo on Consumer Behavior Does music tempo influence consumers’ shopping behavior in retail stores? Retail stores playing fast-tempo music tend to experience increased sales due to consumers’ faster shopping behavior.
Influence of Parenting Style on Academic Success How do different parenting styles impact students’ academic success and motivation? Students raised in authoritative households tend to exhibit higher academic success and intrinsic motivation in school.
Impact of Gender Stereotypes on Career Choices How do gender stereotypes affect individuals’ career choices in traditionally male-dominated fields? Individuals exposed to gender stereotypes are less likely to pursue careers in traditionally male-dominated fields.
Effects of Climate Change on Ecosystems What are the consequences of climate change on ecosystems and biodiversity? Ecosystems exposed to rising temperatures experience shifts in species distribution and increased threats to biodiversity.
Influence of Peer Pressure on Risky Behavior How does peer pressure influence adolescents’ engagement in risky behaviors, such as substance abuse? Adolescents under peer pressure are more likely to engage in risky behaviors like substance abuse compared to those who are not.
Impact of Advertising on Consumer Preferences Does advertising influence consumers’ preferences and purchasing decisions? Consumers exposed to persuasive advertising tend to develop preferences for the advertised products and make purchasing decisions based on the ads.
Effect of Teacher Feedback on Student Performance How does the type of feedback provided by teachers affect students’ academic performance? Students who receive specific and constructive feedback from teachers tend to demonstrate improved academic performance.

Quantitative Research Question and Hypothesis Statement Examples

In quantitative research, researchers aim to collect and analyze numerical data to answer specific research questions. A quantitative research question is designed to be measurable and testable, and it often involves examining the relationship between variables. The corresponding hypothesis statement predicts the expected outcome of the research based on previous knowledge or theories.

Effect of Exercise on Weight Loss How does regular exercise impact weight loss in individuals? Individuals who engage in regular exercise will experience greater weight loss.
Relationship Between Sleep and Productivity Is there a correlation between sleep duration and productivity levels? Longer sleep durations are associated with higher levels of productivity.
Impact of Smartphone Use on Academic Performance How does smartphone use affect students’ academic performance? Increased smartphone use leads to decreased academic performance in students.
Influence of Social Support on Stress How does social support mitigate stress levels in individuals? Higher levels of social support result in lower stress levels among individuals.
Effects of Advertising Frequency on Sales Does the frequency of advertising exposure affect product sales? Higher advertising frequency leads to increased product sales.
Relationship Between Coffee Consumption and Alertness Is there a relationship between coffee consumption and alertness levels? Individuals who consume more coffee tend to experience higher levels of alertness.
Impact of Study Time on Exam Scores How does the amount of time spent studying affect exam scores? Longer study hours are associated with improved exam scores.
Effect of Age on Memory Recall Does age have an impact on memory recall ability? Older individuals exhibit lower memory recall compared to younger ones.
Influence of Price on Consumer Preference How does the price of a product influence consumers’ preferences? Consumers are more likely to prefer products with lower prices.
Relationship Between Screen Time and Sleep Quality Is there a link between screen time and the quality of sleep? Increased screen time before bed is linked to poorer sleep quality.

Psychology Research Question and Hypothesis Statement Examples

Psychology is the scientific study of human behavior and mental processes. Psychology research questions delve into various aspects of human behavior, cognition, emotion, and more. These questions are designed to gain a deeper understanding of psychological phenomena. Hypothesis statements for psychology hypothesis  research predict how certain factors or variables might influence human behavior or mental processes.

Impact of Mindfulness on Stress Reduction How does practicing mindfulness meditation affect individuals’ stress levels? Individuals who engage in mindfulness meditation experience reduced levels of stress.
Relationship Between Parenting Style and Behavior Is there a correlation between parenting styles and children’s behavior? Authoritative parenting is associated with positive behavior outcomes in children compared to other styles.
Effects of Music on Mood and Emotion How does listening to different types of music influence individuals’ mood and emotional states? Upbeat music genres are more likely to improve individuals’ mood and evoke positive emotions.
Influence of Self-Efficacy on Achievement How does individuals’ self-efficacy beliefs affect their academic and professional achievements? Individuals with high self-efficacy tend to achieve greater success in both academic and professional domains.
Impact of Color on Cognitive Performance How does exposure to different colors affect cognitive performance and concentration? Certain colors, like blue and green, enhance cognitive performance and attention compared to others.
Relationship Between Personality and Leadership Is there a link between personality traits and effective leadership skills? Individuals with extroverted and conscientious personality traits tend to exhibit stronger leadership skills.
Effects of Social Media on Body Image How does frequent exposure to social media impact individuals’ body image perceptions? Increased social media use contributes to negative body image perceptions and lowered self-esteem.
Influence of Peer Pressure on Decision Making How does peer pressure influence individuals’ decision-making processes? Individuals under peer pressure are more likely to make decisions against their personal preferences.
Impact of Childhood Trauma on Mental Health Does childhood trauma have lasting effects on individuals’ mental health outcomes? Individuals who experienced childhood trauma are more susceptible to long-term mental health issues.
Relationship Between Empathy and Altruistic Behavior Is there a connection between empathy levels and engaging in altruistic actions? Individuals with higher empathy tend to engage in more frequent acts of altruism towards others.

Testable Research Question and Hypothesis Statement Examples

Testable research questions are formulated in a way that allows them to be tested through empirical observation or experimentation. These questions are often used in scientific and experimental research to investigate cause-and-effect relationships between variables. The corresponding hypothesis statements propose an expected outcome based on the variables being studied and the conditions of the experiment.

Effect of Vitamin C on Immune System Can vitamin C supplementation enhance the immune system’s ability to fight off infections? Individuals taking vitamin C supplements will experience fewer instances of infections.
Relationship Between Study Methods and Grades Is there a correlation between study methods and students’ academic grades? Students who use active study methods will achieve higher grades compared to passive methods.
Impact of Advertisement Placement on Sales How does the placement of advertisements influence product sales in retail stores? Advertisements placed near checkout counters lead to increased product sales.
Influence of Sleep on Reaction Times Does sleep duration affect individuals’ reaction times in cognitive tasks? Individuals with adequate sleep will exhibit faster reaction times in cognitive tasks.
Effects of Temperature on Productivity How does room temperature impact employees’ productivity in an office environment? Comfortable room temperatures enhance employees’ productivity compared to extreme temperatures.
Relationship Between Exercise and Heart Health Is there a link between regular exercise and improved heart health? Individuals who engage in regular exercise have lower risks of heart-related health issues.
Impact of Adjective Use on Persuasion Can the use of positive adjectives enhance the persuasiveness of marketing messages? Marketing messages incorporating positive adjectives lead to greater persuasion effects.
Influence of Background Music on Creativity How does background music affect individuals’ creativity levels during tasks? Background music enhances individuals’ creativity during tasks requiring creative thinking.
Relationship Between Diet and Blood Pressure Is there a correlation between dietary habits and blood pressure levels? Individuals following a low-sodium diet tend to have lower blood pressure readings.
Effect of Leadership Style on Employee Morale How does leadership style impact employee morale in a corporate setting? Transformational leadership fosters higher employee morale compared to autocratic leadership.

Is the Hypothesis Statement and Research Question Statement the Same Thing?

The hypothesis statement and research question statement are closely related but not the same. Both play crucial roles in research, but they serve distinct purposes.

  • Research Question Statement : A research question is a clear and concise inquiry that outlines the specific aspect of a topic you want to investigate. It is often expressed as an interrogative sentence and helps guide your research by focusing on a particular area of interest.
  • Hypothesis Statement : A hypothesis is a testable statement that predicts the relationship between variables. It’s based on existing knowledge or theories and proposes an expected outcome of your research. Hypotheses are formulated for experimental research and provide a basis for collecting and analyzing data.

How Do You State a Research Question and Hypothesis?

Research question :.

  • Identify the topic of interest.
  • Specify the aspect you want to explore.
  • Frame the question as a clear and concise interrogative sentence.
  • Ensure the question is researchable and not too broad or too narrow.

Hypothesis Statement :

  • Identify the variables involved (independent and dependent).
  • Formulate a prediction about their relationship.
  • Use clear language and avoid ambiguity.
  • Write it as a declarative statement.

How Do You Write a Research Question and Hypothesis Statement? – A Step by Step Guide

  • Identify the Topic : Choose a specific topic that interests you and is relevant to your field of study.
  • Background Research : Gather information about existing research related to your topic. This helps you understand what’s already known and identify gaps or areas for exploration.
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  • Published: 24 July 2024

Single-cell multiregion dissection of Alzheimer’s disease

  • Hansruedi Mathys   ORCID: orcid.org/0000-0003-0186-2115 1 , 2 , 3 , 4   na1 ,
  • Carles A. Boix   ORCID: orcid.org/0000-0001-9212-856X 5 , 6 , 7   na1 ,
  • Leyla Anne Akay   ORCID: orcid.org/0000-0002-5944-2466 1 , 2   na1 ,
  • Ziting Xia   ORCID: orcid.org/0009-0003-6666-7430 1 , 2 , 8 ,
  • Jose Davila-Velderrain   ORCID: orcid.org/0000-0003-0271-6267 9 ,
  • Ayesha P. Ng 1 , 2 ,
  • Xueqiao Jiang 1 , 2 ,
  • Ghada Abdelhady 3 ,
  • Kyriaki Galani 5 , 6 ,
  • Julio Mantero 5 , 6 ,
  • Neil Band 5 , 6   nAff12 ,
  • Benjamin T. James   ORCID: orcid.org/0000-0002-6228-055X 5 , 6 ,
  • Sudhagar Babu   ORCID: orcid.org/0000-0001-6012-8936 3 ,
  • Fabiola Galiana-Melendez 1 , 2 ,
  • Kate Louderback 1 , 2 ,
  • Dmitry Prokopenko 10 ,
  • Rudolph E. Tanzi   ORCID: orcid.org/0000-0002-7032-1454 10 ,
  • David A. Bennett 11 ,
  • Li-Huei Tsai   ORCID: orcid.org/0000-0003-1262-0592 1 , 2 , 6 &
  • Manolis Kellis   ORCID: orcid.org/0000-0001-7113-9630 5 , 6  

Nature ( 2024 ) Cite this article

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  • Alzheimer's disease
  • Gene expression
  • Molecular neuroscience

Alzheimer’s disease is the leading cause of dementia worldwide, but the cellular pathways that underlie its pathological progression across brain regions remain poorly understood 1 , 2 , 3 . Here we report a single-cell transcriptomic atlas of six different brain regions in the aged human brain, covering 1.3 million cells from 283 post-mortem human brain samples across 48 individuals with and without Alzheimer’s disease. We identify 76 cell types, including region-specific subtypes of astrocytes and excitatory neurons and an inhibitory interneuron population unique to the thalamus and distinct from canonical inhibitory subclasses. We identify vulnerable populations of excitatory and inhibitory neurons that are depleted in specific brain regions in Alzheimer’s disease, and provide evidence that the Reelin signalling pathway is involved in modulating the vulnerability of these neurons. We develop a scalable method for discovering gene modules, which we use to identify cell-type-specific and region-specific modules that are altered in Alzheimer’s disease and to annotate transcriptomic differences associated with diverse pathological variables. We identify an astrocyte program that is associated with cognitive resilience to Alzheimer’s disease pathology, tying choline metabolism and polyamine biosynthesis in astrocytes to preserved cognitive function late in life. Together, our study develops a regional atlas of the ageing human brain and provides insights into cellular vulnerability, response and resilience to Alzheimer’s disease pathology.

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Alzheimer’s disease (AD) is characterized by pathological protein aggregation in a stereotyped pattern across multiple brain regions 1 , 4 . Post-mortem diagnosis of AD is staged by the severity and distribution of these pathological hallmarks: extracellular amyloid-β deposits and intracellular neurofibrillary tangles (NFTs) in neurons. Tangles are first seen in the entorhinal cortex (EC) (Braak stages I–II), then the hippocampus and thalamus (Braak stages III–IV) and finally the neocortex (Braak stages V–VI), a sequence that is typically synchronous with cognitive decline from mild cognitive impairment to severe dementia 1 , 2 , 4 , 5 , 6 , 7 . Understanding the cellular architecture of affected brain regions has important implications for early and region-specific therapeutic interventions and may shed light on the molecular mechanisms underlying the regional progression of pathology. Although some brain regions relevant to AD have been studied individually at scale or jointly in samples from a few individuals 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , a comprehensive molecular characterization of region-specific differences in AD is currently lacking and could capture differences in regional molecular architecture 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 and region-specific neuronal and glial subtype alterations in AD and in cognitive resilience to AD pathology 3 , 25 , 26 , 27 .

Here we present a transcriptomic atlas of the human brain spanning six distinct anatomical regions from persons with and without Alzheimer’s dementia as a basis for understanding disease-associated differences. We profile the transcriptomes of over 1.3 million nuclei from the EC, hippocampus (HC), anterior thalamus (TH), angular gyrus (AG), midtemporal cortex (MT) and prefrontal cortex (PFC) from 48 individuals, 26 of whom have a pathologic diagnosis of AD. We annotate region-specific neuronal and glial subtype diversity, present an online resource for navigating this atlas ( http://compbio.mit.edu/ad_multiregion ) and provide mechanistic insights into cellular vulnerability, response and resilience to AD.

A multiregion atlas of AD

To characterize cellular diversity in the human brain, and the genes, pathways and cell types that underlie AD progression across brain regions, we performed single-nucleus RNA-sequencing (snRNA-seq) analysis of nuclei isolated from 283 post-mortem brain samples across six brain regions from 48 participants in the Religious Order Study (ROS) or the Rush Memory and Aging Project (MAP) 28 (together, ROSMAP; Fig. 1a ). We selected 48 participants on the basis of pathologic diagnosis of AD (stratified by NIA-Reagan score of 26 (with AD) and 22 (without AD; labelled non-AD)) and on the basis of clinical diagnosis of Alzheimer’s dementia ( n  = 16) versus non-dementia ( n  = 32) 29 , 30 (Fig. 1a , Extended Data Fig. 1a and Supplementary Table 1 ). From these 48 individuals, we profiled six brain regions: the EC (221,493 cells), which is affected in early AD (stages I–II); the HC (221,415) and TH (207,625), which are affected in mid-AD (stages III–IV); and the AG (220,409), MT (227,412) and PFC (254,721), which are affected in late AD (stages V–VI), for a total of 1.35 million transcriptomes of independent nuclei after removing doublets, low-quality cells and highly sample-specific clusters. We annotated 76 high-resolution cell types in 14 major cell type groups, including 32 excitatory neuron subtypes (436,014 nuclei, 32.2% of total) and 23 inhibitory subtypes (159,838 nuclei, 11.8% of total) (Extended Data Fig. 1b–d , Supplementary Figs. 1 and 2 and Supplementary Table 2 ). We characterized these cell types in terms of their transcriptome size and proliferative status, compared our atlas with previously published data across species 31 , 32 , 33 (Extended Data Fig. 1e,f and Supplementary Figs. 3 – 5 ) and identified broad cell type identity programs using non-negative matrix factorization (NMF) 34 and transcriptional regulons using SCENIC 35 , 36 (Extended Data Figs. 2 and 3 and Supplementary Tables 3 and 4 ).

figure 1

a , snRNA-seq profiling summary, covering 283 samples across 6 brain regions from 48 participants from ROSMAP, showing global pathology, Braak stage and pathological (26 AD and 22 non-AD) or clinical diagnosis of AD (16 AD dementia (dem.) and 32 no dementia). b , c , Joint uniform manifold approximation and projection (UMAP), coloured by major cell type ( b ) and region of origin ( c ). d , The regional composition of major cell types. e , Relative enrichment of major cell types across regions by quasi-binomial regression. False discovery rate (FDR)-corrected P values are indicated by asterisks; *** P  < 0.001, ** P  < 0.01, * P  < 0.05. f , g , Global breakdown, region composition, enrichment and number of nuclei for excitatory ( f ) and inhibitory ( g ) neuronal subtypes. h , Gene expression analysis of the top four markers per inhibitory subclass, averaged at the sample by subclass level (columns). i , RNAscope validation of FOXP2 and MEIS2 as markers of the unique thalamus subtype, with quantification (left) performed using Student’s t -tests and representative images (right). The blue puncta represent MEIS2 (top) or FOXP2 (bottom) transcripts and red puncta represent GAD2 transcripts. FOXP2 : n  = 19 (PFC) and n  = 22 (TH) cells; MEIS2 : n  = 35 (PFC) and n  = 26 (TH) cells; each dot represents an individual cell, pooled from eight samples (four individuals; each had one PFC and one thalamus sample). j , Glutamatergic versus GABAergic scores for all neuron subtypes. The dotted lines represent the 95% confidence interval around the linear fit. P values were calculated using two-sided F tests. Ast., astrocytes; exc., excitatory neurons; inh., inhibitory neurons; mic., microglia/immune cells; olig., oligodendrocytes; vasc., vascular/epithelial cells.

To gain insights into the cellular architecture of the human brain, we investigated differences in the composition of major cell types between the six brain regions. The fraction of neurons increased significantly from the TH (14.4% neurons) to the three-layer allocortical HC (32.2%), the entorhinal periallocortex (36.6%) and the six-layered neocortical regions (AG, MT and PFC, 58.9%) (Fig. 1b–e and Supplementary Fig. 6 ). Glia, including astrocytes, oligodendrocytes, oligodendrocyte precursor cells (OPCs) and microglia/immune cells, tended to be less abundant in neocortical samples (Fig. 1b–e ), in agreement with previous studies in humans 37 , 38 and mice 39 , 40 (Supplementary Fig. 7a–d ). Differences in the composition of major cell types between regions were reproducibly observed across study participants, irrespective of the individual’s disease status (Supplementary Fig. 7e–h ), suggesting that variability in the major cell type composition between regions is a fundamental characteristic of the human brain and is not affected by AD pathology.

Neuronal diversity across brain regions

We first characterized the regional diversity of excitatory neuron subtypes, which were consistent across individuals and were either highly region-specific to the HC, EC and TH (7, 9 and 2 subtypes, respectively) or were predominantly shared across neocortical regions (12 subtypes) (Fig. 1f and Supplementary Fig. 8 – 12 ). Hippocampal subtypes included neurons from the highly structured CA1 and CA2/CA3 subfields and dentate gyrus and the more entorhinal-proximal subiculum and para/presubiculum areas 9 . EC-specific subtypes that clustered separately from neocortical subtypes for the same layers were often marked by expression of RELN , TOX3 and GPC5 , and contained subtypes from both the lateral (L2 RELN + GPC5 + ) and medial (L2 TOX3 + POSTN + ) EC 41 , 42 , 43 (Supplementary Fig. 10 ). Excitatory neurons in the TH were predominantly composed (74%) of a subtype ( NXPH1 + RNF220 + ) that was not observed in the neocortex and is predicted to be regulated by LHX9 , SOX2 , SHOX2 and TCF7L2 34 , 36 (Extended Data Fig. 2a,b and Supplementary Figs. 9e–i and 11n,o ). We found that the thalamic–neocortex separation is conserved in mice and recapitulated both this divide and thalamic marker genes in independent single-cell, bulk and microarray data in both mice and humans 8 , 39 , 40 , 43 (Supplementary Fig. 12 ).

In contrast to excitatory neuron subtypes, the majority of inhibitory neuron subtypes (22 out of 23 subtypes) were observed in all five cortical regions (Fig. 1g and Supplementary Figs. 13 – 17 ), although some inhibitory subtypes had regional biases, including PVALB + HTR4 + and CUX2 + MSR1 + (enriched in neocortex), layer 6 SST + NPY + (EC and HC) and GPC5 + RIT2 + (EC), suggesting that there are significant differences in inhibitory neuron composition between the neocortex and allocortex (Fig. 1g and Supplementary Fig. 14 ). Moreover, in the HC, EC and MT, caudal ganglionic eminence-derived GABAergic neurons ( VIP + LAMP5 + ) were significantly more abundant than medial ganglionic eminence-derived neurons ( SST + PVALB + ), but these two major clades were not significantly different in the PFC (Extended Data Fig. 1g ). By contrast, the TH contained a single unique, thalamus-specific inhibitory subtype ( MEIS2 + FOXP2 + ) marked by genes that are involved in neurite outgrowth, such as the semaphorins SEMA3C and SEMA3E , DISC1 and SPON1 , and receptors for serotonin ( HTR2A ), acetylcholine ( CHRM2 , CHRNA3 ) and glutamate ( GRM3 ) (Fig. 1g,h and Supplementary Figs. 14 and 15 ). These genes were in a single inhibitory program (Inh-22, from NMF) that included the SCENIC-predicted subtype regulators FOXP2 and LEF1 34 , 36 (Extended Data Figs. 2c,d and 3b ). We recapitulated this thalamic difference and program genes in the mouse thalamus and human lateral geniculate nucleus (dLGN) using previously published single-cell data (Supplementary Figs. 16 and 17 ). To validate the localization and specificity of markers of the thalamic inhibitory neuron subtype, we performed in situ hybridization for both FOXP2 and MEIS2 with GAD2 on TH and PFC post-mortem brain samples from four individuals, and found significant thalamus-specific co-localization of both marker genes with GAD2 (Fig. 1i ).

As thalamic MEIS2 neurons expressed several typically glutamatergic neuron genes, we determined glutamatergic and GABAergic module scores for every neuronal cell to further examine the chimeric nature of this subtype (Supplementary Fig. 15g–k and Supplementary Table 5 ). These scores matched the cortical excitatory and inhibitory split and were negatively correlated both across and within broad neuronal classes (Fig. 1j and Supplementary Fig. 15g,h ). Both thalamic MEIS2 + inhibitory and NXPH1 + excitatory neurons had intermediate scores, placing them between the cortical excitatory and inhibitory clusters, suggesting that they are less polarized with regard to the expression of cortical glutamatergic versus GABAergic programs (Fig. 1j and Supplementary Fig. 15i–k ). Predicted cell–cell communication interactions were mostly shared across multiple regions, but the thalamus had multiple differential interactions (Supplementary Figs. 18 and 19 ). The top thalamus-specific interactions were between excitatory NXPH1 and neuronal NRXN1 or NRXN3 , whereas inhibitory neurons expressed NXPH1 in the other regions, suggesting that neurexophilin signalling swaps from excitatory neurons in the thalamus to inhibitory neurons in cortical brain regions (Extended Data Fig. 4 ).

Glial diversity annotated by gene modules

We next tested whether glial cells also had transcriptional differences between brain regions. We identified multiple transcriptionally distinct subsets for each major glial cell type and determined their characteristic marker genes (Fig. 2a and Supplementary Fig. 20 – 25 ). Among glial cell types, astrocytes had the highest regional heterogeneity, containing both highly neocortex-enriched ( GRM3 + DPP10 + ) and thalamus-enriched ( LUZP2 + DCLK1 + ) subtypes (Fig. 2a–c and Supplementary Fig. 20 ). Region-specific astrocyte subtypes were experimentally validated using RNA in situ hybridization (Fig. 2d ) and confirmed by analysing a separate snRNA-seq dataset 14 (Supplementary Fig. 23m ). Cortical astrocytes were enriched for markers involved in glutamate processing and transport, whereas hippocampus- and anterior thalamus-enriched DCLK1 astrocytes had lower glutamate transporter activity and were enriched instead for focal-adhesion-related genes (Fig. 2c and Supplementary Fig. 25a ). Thalamic astrocytes ( LUZP2 + ) expressed GABA-uptake genes SLC6A1 and SLC6A11 at much higher levels compared with other subtypes, even though the proportion of inhibitory neurons was not markedly higher in the thalamus (Fig. 2c ). Notably, the thalamic MEIS2 + FOXP2 + interneurons shared multiple markers with neocortical GRM3 astrocytes, including GRM3 , MEIS2 and VAV3 39 , 40 , 43 (Supplementary Fig. 23n ), suggesting that astrocytes in evolutionarily newer regions may share some functions with inhibitory neurons in older regions.

figure 2

a , UMAP plot for astrocyte nuclei, coloured by astrocyte subtype or brain region of origin. b , Global breakdown and regional composition of astrocyte subtypes. c , Gene expression heat map for the top markers of each astrocyte subclass, averaged to sample by subtype and scaled to the row maximum (max.). d , RNAscope validation of GRM3 and LGR6 as markers of AQP4 + neocortical and TH astrocytes, respectively (bold markers in c ). Representative images (left) showing AQP4 transcripts (blue puncta) and GRM3 or LGR6 transcripts (red puncta). Scale bars, 20 μm. Quantification (right) was performed using two-tailed unpaired Student’s t -tests; **** P  < 0.0001. Each dot represents an individual cell, pooled from eight samples (four individuals; each with one PFC and one thalamus sample). GRM3 : n  = 37 (PFC) and n  = 23 (TH) cells; LGR6 : n  = 17 (PFC) and n  = 23 (TH) cells. e , The framework for detecting gene expression modules using scdemon. f , The number of modules enriched for each covariate across all module sets (hypergeometric test, P  < 0.001). Bar plots are coloured by the covariate level for which the modules are enriched (or by the major cell type used for module discovery for cell subtype). Diag., diagnosis. g , h , Gene–gene network ( g ) and magnification of the indicated regions ( h ) for astrocyte modules, with insets for M19, a subtype identity module for LUZP2 astrocytes ( h , left) and M17, a functional program involved in cholesterol biosynthesis ( h , right). AA, amino acid. i , Contour plots on the astrocyte UMAP for module expression of five identity (top row) and five functional (bottom row) programs. Expression was smoothed on a 500 × 500 grid with a 2D Gaussian kernel (size = 25 × 25; σ  = 1). j , k , Module contours showing regions of top expression on the astrocyte UMAP for selected identity modules ( j ) and corresponding module scores ( k ) for the 18 labelled representative cells across the astrocyte UMAP for selected identity and expression models, scaled to the maximal expression of each module. ER, endoplasmic reticulum; SVD, singular value decomposition.

We developed a method, single-cell decorrelated module networks (scdemon), to identify gene expression modules from highly correlated sets of genes in atlas-scale snRNA-seq datasets (Fig. 2e ). Highly imbalanced cell type composition in single-cell datasets, in which rare cellular states are outnumbered by common cell types, can lead to under-recovery of gene–gene interactions, especially for genes that are expressed at low levels. To account for these issues, our method estimates a sample-decorrelated gene–gene correlation matrix, thresholds gene–gene pairs based on their sparsity and uses the adjusted matrix to identify modules of highly correlated genes ( Methods ). We used our method to identify modules both across all cells in the atlas and for each major cell type independently, and recovered modules expressed to varying degrees, ranging from identity modules for each glial cell type to a cell cycle module found in just 0.7% of microglia (Fig. 2f , Extended Data Fig. 5 , Supplementary Figs. 26 – 36 and Supplementary Table 6 ). Cells expressing these modules were enriched for diverse aspects of our dataset, including cellular subtype identity (205 modules), brain region (156, with 77 thalamus specific and 34 EC specific), AD status (73), APOE genotype (78) and sex (24) (Fig. 2f and Supplementary Table 7 ). We hierarchically clustered modules across the cell types and found that many cell types expressed gene programs for cholesterol biosynthesis (C10), chaperones (C5), ribosomes (C1 and C2), ER protein processing (C7), oxidative phosphorylation (C18), synapse interaction (C16), and glycolysis and response to hypoxia (C20) (Extended Data Fig. 6a,b ).

Using this approach, we identified 32 modules in astrocytes, including an astrocyte-wide program (M9, expressed in >99% of astrocytes) marked by GPM6A and GPC5 and enriched for cell junction assembly, and subtype- and region-specific identity programs such as thalamus-associated M19 ( SLC6A11 , LGR6 , MRAS ), which were enriched for sonic hedgehog signalling, M12 ( GRM3 : forebrain neuron development) and M7 ( DCLK1 : synaptic membrane) (Fig. 2g,h and Supplementary Fig. 31 ). Other modules spanned a diverse set of functions, including metallostasis, RNA splicing, glycolysis, oxidative phosphorylation and cholesterol biosynthesis and were shared by multiple subtypes (Fig. 2i–k and Extended Data Figs. 5b and 6a–c ). For example, chaperone-enriched and APOE-ε4-associated M8 was expressed in multiple different astrocyte subtypes and regions, and expression of AD-associated M28 (metallostasis) overlapped with expression of both APOE + (M0) and reactive (M3) astrocytes (Fig. 2i–k ). Module–module correlations across samples revealed co-expressed programs, such as reactive astrocytes (M3, marked by TPST1 , CLIC4 and EMP1 ) with cholesterol biosynthesis module M17 ( r  = 0.60), and glycolysis (M6) with AP-1 module M13 ( r  = 0.39, including FOS / JUN and ubiquitin), a pair that is potentially co-expressed in astrocytes under metabolic stress (Extended Data Fig. 6d,e ).

In contrast to astrocytes, immune cells showed little regional specificity and oligodendrocyte-lineage cells had thalamus-enriched subtypes with minor transcriptomic differences to neocortex-enriched subtypes (Supplementary Figs. 21 – 25 ). Immune modules included identity programs, such as for T cells (M6), macrophages (M7) and cycling microglia ( MKI67 + , M5) as well as modules found across immune cells and enriched for genes involved in NF-κB signalling (M18), interferon (M20), p53 and DNA damage response (M22) and TGFβ signalling (M14) (Extended Data Fig. 6f and Supplementary Fig. 32 ). Oligodendrocyte-lineage modules showed high regional specificity, and two OPC modules—thalamus-enriched M11 and EC-enriched M25—were marked by synapse-associated genes such as neural adhesion-related SEMA3D , SEMA6D and CNTN5 , and glutamate receptor GRIA4 , suggesting a role for OPC sensation and response to neuronal activity in specific brain regions (Extended Data Fig. 5c,e and Supplementary Figs. 33 , 34 and 36 ).

Vulnerable neuronal subtypes in AD

After constructing our atlas across AD-affected brain regions, we examined how AD affects the cellular composition. At the level of major cell types, we observed slight, non-significant decreases in the number of both excitatory neurons (odds ratio (OR) = 0.94, individuals stratified by pathologic diagnosis of AD), inhibitory neurons (OR = 0.93) and OPCs (OR = 0.85), as well as an increase in the number of oligodendrocytes (OR = 1.14, adjusted P ( P adj ) = 0.01) and vascular cells (OR = 1.24), mostly driven by differences in the EC, HC and PFC regions, especially in late AD (Extended Data Fig. 7a,b ). We next tested whether the fractions of region-specific neuronal subtypes were significantly altered relative to both individual-level pathologic and clinical diagnoses of AD and region-level NFT and plaque accumulation (Fig. 3a and Extended Data Fig. 7c,d ). Among excitatory neurons, we identified one HC-specific (CA1 pyramidal neurons) and four EC-specific (L2 RELN + lateral EC, L3 RELN + , L5 and L2/3 TOX3 + TTC6 + neurons) subtypes that were significantly less abundant (OR = 0.38–0.66) in individuals with a pathologic diagnosis of AD (Fig. 3a and Supplementary Fig. 37a–c ). Neocortical L2–3 neurons were also significantly less abundant in samples with high NFT levels and in individuals with neocortical NFT involvement (Fig. 3a ). Individuals with lower percentages of these vulnerable excitatory neuron subtypes performed significantly worse on cognitive tasks, with the strongest observed impacts on episodic memory and global cognitive function for subtypes marked by GPC5 (EC L5 and L2 RELN + ) 2 (Extended Data Fig. 7e,f ). Notably, while the overall excitatory fraction was not associated with cognition, lower OPC fraction across regions and, in particular, in non-neocortex regions was significantly associated with impaired cognition (Supplementary Fig. 37d ).

figure 3

a , Compositional differences in excitatory neuron subtype enrichment and depletion in AD by quasi-binomial regression with FDR correction. Clin. diag., clinical diagnosis; path. AD, pathologic AD. b , Scatter plot and correlations (Kendall’s τ ) of the subtype fraction between four pairs of neuronal subtypes in the HC and EC (linear fit with 95% confidence intervals). c , Schematic of the HC and EC, highlighting the locations of vulnerable excitatory subtypes and co-depleted connections. d , Genes associated with excitatory neuron subtype vulnerability across all brain regions. Linear regression between normalized sample + subtype-level gene expression and log 2 [OR] for late-AD, with FDR-corrected P values. e , Genes associated with excitatory and inhibitory subtype vulnerability (FDR-corrected P values, only genes significantly and positively associated with excitatory subtype vulnerability). f , Schematic of Reelin signalling pathway genes that are differentially expressed in vulnerable inhibitory subtypes (colour indicates the log 2 -transformed fold change in expression between vulnerable and non-vulnerable subtypes). The diagram was created using BioRender. g , In situ hybridization (RNAscope) validation of depletion of RELN + excitatory neurons in the EC of individuals with AD relative to individuals without AD. Representative images (left) include Hoechst (blue), vGlut transcripts (green puncta) and RELN transcripts (magenta puncta). Scale bars, 20 μm. Quantification (right) was performed using unpaired two-tailed Student’s t -tests ( P  = 0.0242). Data are mean ± s.e.m. n  = 5 (non-AD) and n  = 4 (AD) individuals. h , i , Immunohistochemistry analysis of Reelin, NeuN and amyloid-β ( h ) or phosphorylated tau ( i ) in 12-month-old App-KI mice ( h ) or 9-month-old Tau(P301S) transgenic mice ( i ), showing depletion of Reelin-positive neurons in the ECs of the KI and transgenic mice compared with those of the wild-type controls. Representative images (left) show Hoechst (blue); amyloid-β ( h ; D54D2) or phosphorylated-tau ( i ) (green); NeuN (yellow); and Reelin (red). Scale bars, 100 μm ( h and i ). Quantification (right) was performed using unpaired two-tailed Student’s t -tests; P  = 0.0181 ( App -KI, h ; n  = 7 ( App -KI) and n  = 6 (wild type) mice) and P  = 0.0005 (Tau(P301S), i ; n  = 6 mice (Tau(P301S)) and n  = 5 (wild type) mice). Data are mean ± s.e.m. ParaS, parasubiculum; PrS, presubiculum.

Source Data

Given that these neuronal subtypes lie in highly interconnected regions, we next examined whether neuronal subtypes connected across regions were coordinately depleted. We found that vulnerable neuronal subtypes were co-depleted specifically in individuals with AD, with some of the strongest effects observed in established connections between the CA1, subiculum, EC–L3 and EC–L5 (Fig. 3b,c and Extended Data Fig. 7g ). These included co-depletion for entorhinal L5 versus L5-projecting subiculum (Kendall’s τ  = 0.37 (AD); −0.1 (non-AD)) or CA1 ( τ  = 0.42 (AD) and −0.16 (non-AD)); and for CA1 versus L2-lateral EC (LEC,  τ  = 0.26 (AD) and −0.07 (non-AD)) and L3 RELN + ( τ  = 0.24 (AD) and −0.13 (non-AD)) EC neurons, both of which project in part to the CA1 subfield 44 , 45 (Fig. 3b,c and Extended Data Fig. 7g ).

We next investigate whether vulnerable subtypes share marker genes that might mediate their vulnerability, and identified 391 genes with significantly higher baseline (non-AD) expression in vulnerable subtypes (Fig. 3d and Supplementary Table 8 ). These included Reelin signalling pathway genes RELN and DAB1 ; kinase-associated genes MAP2K5 , PRKCA and SPHKAP ; and multiple genes associated with heparan sulfate proteoglycan biosynthesis (including HS6ST3 , XYLT1 and NDST3 ) (Fig. 3d and Extended Data Fig. 7h,i ). Notably, while RELN expression, which is typically restricted to inhibitory neurons, was highly specific to two EC excitatory subtypes, its downstream partner DAB1 was present across subtypes (Extended Data Fig. 7h,i and Supplementary Fig. 37e,f ).

We next examined whether vulnerable inhibitory neuron subtypes in the PFC share characteristics with vulnerable excitatory neuron subtypes across our brain regions using single-cell transcriptomes from 621 ROSMAP study participants 27 , 46 . We identified specific inhibitory neuron subtypes that are depleted in individuals with a high tangle density burden, consistent with our previous findings 27 (Extended Data Fig. 7j ). Vulnerable and non-vulnerable inhibitory neuron subtypes differed in the expression of genes involved in neuron projection morphogenesis ( ROBO2 , SEMA6A and EPHB6 ), enzyme-linked receptor protein signalling pathways ( FGFR2 , TGFBR1 and PLCE1 ) and heparan sulfate proteoglycan biosynthesis (Extended Data Fig. 7k and Supplementary Table 8 ). Notably, vulnerable inhibitory neuron subtypes expressed significantly higher levels of the Reelin signalling pathway components RELN and DAB1 , mirroring the observed higher expression of these two genes in vulnerable excitatory neuron subtypes (Fig. 3e ). Furthermore, the Reelin receptors LRP8 (also known as ApoER2) and NRP1 exhibited significantly different baseline expression in vulnerable compared with non-vulnerable inhibitory neuron subtypes (Fig. 3f ).

To test the selective vulnerability of Reelin-expressing excitatory neurons in AD, we performed in situ hybridization (RNAscope) analysis of Reelin and vGlut (excitatory neuron marker) in EC tissue samples from both patients with AD and healthy individuals without AD. We found a significant decrease in the percentage of Reelin-expressing excitatory neurons in the EC of individuals with AD (Fig. 3g ). To determine whether this finding was conserved in animal models of AD, we used immunohistochemistry to assess the expression of Reelin in the EC of both 12-month-old App knock-in (KI) mice and 9-month-old Tau(P301S) transgenic mice. We found that, relative to wild-type littermate controls, App -KI mice and Tau(P301S) mice had a significantly decreased percentage of Reelin-positive neurons in the EC (Fig. 3h,i ), in agreement with our human transcriptomic data suggesting a selective vulnerability of Reelin-expressing neurons (Fig. 3d–f ).

To understand how vulnerable subtypes are altered in AD, we computed differentially expressed genes (DEGs) for each excitatory neuron subtype ( Methods and Supplementary Fig. 38a–c ). We partitioned DEGs into sets associated with either vulnerable or non-vulnerable subtypes according to their expression levels in individuals with late AD (Extended Data Fig. 7l,m ). DEGs linked to non-vulnerable subtypes were enriched for a diverse set of functions, including ubiquitin-ligase binding, heat-shock-family chaperones, ER protein processing and mediators of neuronal death, whereas vulnerability-associated DEGs were highly enriched only for mitochondrial oxidative phosphorylation but included CRK and NEUROD2 , which are both associated with Reelin signalling 17 , 18 (Extended Data Fig. 7l,m and Supplementary Fig. 38d–f ). Some DEGs associated with non-vulnerable subtypes had higher differential effect sizes in the vulnerable subtypes, and showed additional enrichment for aerobic glycolysis (including PGK1 , LDHB and SLC2A3 ) and clathrin-mediated endocytosis (including AP2M1 / AP2S1 , OCRL and COPS8 ) (Extended Data Fig. 7m ).

Regional expression differences in AD

To identify regional differences in cellular expression and function specific to individuals with pathologic AD, we computed DEGs for each major cell type in every region alone and across regions using a negative binomial linear mixed model framework, adjusting for both known covariates and potential unknown batch effects ( Methods ) (Extended Data Fig. 8a and Supplementary Table 9 ). Astrocytes and inhibitory and excitatory neurons showed the highest number of DEGs over all of the regions, with the largest number of changes in the EC (Extended Data Fig. 8a ). Notably, neuronal DEGs showed little overlap across regions, indicating that neuronal differences in AD are primarily determined by subtype or region of origin (Extended Data Fig. 8b ). By contrast, microglia and OPC DEGs overlapped within the non-neocortex regions, and astrocyte and oligodendrocyte changes were more consistent across all regions (Extended Data Fig. 8b ). AD DEGs were consistent with published results both for region-specific DEGs and for DEGs computed jointly over all regions for multiple AD variables, and were further corroborated by comparisons with various independent studies 11 , 12 , 15 , 19 , 47 , 48 , 49 , 50 , 51 , 52 , 53 (Supplementary Fig. 39 ).

Excitatory DEGs were strongly enriched for electron-transport functional terms across regions and showed weak region-specific enrichments for protein-folding-, ubiquitination- and synapse-associated terms (Extended Data Fig. 8c ). Inhibitory DEGs were also broadly enriched for protein-folding- and synapse-associated terms and for oxidative phosphorylation uniquely in the thalamus (Extended Data Fig. 8c ). While microglia DEGs were broadly enriched for clathrin-coated endocytosis (up) and viral response (down), they also had diverse region-specific enrichments, including upregulation of major histocompatibility complex type II (MHC-II) binding in the EC and HC, RNA processing in thalamus and glycolysis in the PFC and EC; and HC-driven downregulation of phagocytosis, phospholipase signalling and protein kinase activity (Extended Data Fig. 8c ).

The majority of region-specific DEGs was either broadly shared (on average, 11% of genes were differentially expressed in 3+ cell types in a region) or were in cell-type-specific programs (40% of DEGs were in 3+ regions for a cell type) (Extended Data Fig. 8d,e ). Such genes included SLC38A2 and EIF4G2 (broadly shared across regions) and PRDX5 , HLA-DRA or CD44 , upregulated DEGs in excitatory neurons, microglia and astrocytes, respectively (Extended Data Fig. 8f and Supplementary Fig. 40 ). Broadly shared genes across cell types showed region-specific enrichment, including for DNA damage (EC), amyloid-β binding and iron transport (HC) and glycolysis (thalamus) in upregulated genes as well as for phospholipid biosynthesis and autophagy in downregulated genes (Extended Data Fig. 8e ). Gene sets based on DEGs for global AD pathology burden in the PFC across 427 individuals changed consistently in each region and glial cell type across global pathology, indicating that a significant component of the glial AD response is consistent across regions 27 (Extended Data Figs. 8b–e and 9a,b ). The remaining regional DEGs (on average, 48% of DEGs) highlighted region- and cell-type-specific changes. In microglia, these included PPARG and MSR1 , upregulated in the HC, each associated with microglia polarization, as well as upregulation of lipoprotein modifier APOC1 and downregulation of transcription factor FOXP2 in the EC (Extended Data Fig. 8f and Supplementary Fig. 40 ).

We next examined which cell types and regions were most enriched for genes identified in genome-wide association studies (GWASs) of AD by computing GWAS scores for each cell using single-cell disease-relevance score (scDRS) 54 , 55 . Microglia and immune cells showed consistently high scores across regions, with the top scores for the microglia TPT1 + subtype and macrophages in the HC, thalamus and AG (Extended Data Fig. 9c ). We examined whether GWAS genes showed region-specific differences in expression that might be linked to the region specificity of AD progression. We identified eight GWAS genes with region-specific expression in microglia, including PLCG2 (EC), APOE and SORL1 (thalamus), and MS4A4A (midtemporal cortex) (Extended Data Fig. 9c–f ).

To determine whether GWAS-identified genes have regional associations with Alzheimer’s pathology, we intersected DEGs for regional pathology measurements with 149 identified familial AD and GWAS locus genes 56 , 57 , 58 (Extended Data Figs. 10 and 11a ). We found that 74 genes (49%) were differentially expressed for at least one cell type, and multiple genes showed region-specific expression, including the lipid transporter ABCA7 (enriched in thalamus), the zinc-finger protein ZNF655 (EC) and the complement receptor CR1 (neocortex) 56 (Extended Data Fig. 10 ). GWAS and familial AD genes were maximally expressed (75 genes) and differentially expressed (30 genes) in microglia, and 25 genes were differentially expressed in at least three cell types, including upregulated CLU , PLCG2 and SORT1 , and downregulated DENND6A (Extended Data Fig. 10 ). Among all of the cell types, astrocytes and microglia showed the largest differential changes for these genes in regions with high neuritic plaque density, for example, for APOE , HLA-DRA , PILRA and SORT1 , and showed the most response to diffuse plaque. Neurons and oligodendrocyte-lineage cells showed stronger differences for these genes, including for PLCG2 , CLU and MAF , in regions with high NFT density (Extended Data Fig. 10 ).

Pathology-specific expression changes

To determine whether different pathologies induce distinct transcriptional responses, we computed DEGs for region-specific measurements of NFT and neuritic amyloid-β plaque burden (measured in each region except thalamus) (Fig. 4a , Extended Data Fig. 11a,b and Supplementary Fig. 41 ). DEGs for AD pathology showed a high overlap with DEGs for pathologic diagnosis (NFT: 45% and plaque: 53% on average) (Fig. 4a ). Agreement between NFT and plaque DEGs was highest in the EC and HC for all cell types (average adjusted R 2 of 67% in both) and lowest in the PFC (43%) and AG (21%), consistent with late-AD NFT appearance in the neocortex (Fig. 4b ).

figure 4

a , The percentage of AD DEGs (pathologic diagnosis) overlapping with DEGs for neuritic plaques (neu. plaq.) and NFTs in each major cell type and region. b , Concordance of effect-sizes between neuritic plaque and NFT DEGs. Adjusted R 2 of log-transformed fold changes between neuritic plaque and NFT DEGs in each major cell type and region. c , The number of neuritic-plaque- or NFT-biased DEGs (≥3 DEGs for one of plaques or NFTs, and ≤2 for the other) for each major cell type or shared across 2+ cell types. d – i , The average effect sizes for NFTs and neuritic plaques for DEGs with biased differential effect sizes ( d , f , h ) and their respective functional enrichments ( e , g , i ), for DEGs shared across multiple cell types ( d , e ), in excitatory neurons ( f , g ) or in astrocytes ( h , i ). j , Enrichments (hypergeometric test) of pathology-biased DEGs in astrocyte modules. k , Enrichments (enr.) of AD DEGs in glial gene expression modules (* P adj  < 0.05, signed log 2 [fold change], only significant modules are shown). l , Pearson correlation of module scores in each region with region-level pathology measures for glycolysis and oxidative phosphorylation modules in astrocytes, microglia and OPCs ( # P < 0.1). m , Core and selected diffuse plaque (diff. plaq.) DEGs in glial glycolysis-associated modules. n , Schematic of the glycolysis pathway, annotated by astrocyte diffuse plaque DEGs. Significant DEGs for diffuse plaques across all regions are indicated by asterisks. o , p , RNAscope validation of astrocyte energy metabolism DEGs in the AG of individuals with AD relative to control individuals without AD (pathologic diagnosis of AD). Representative images (left) show AQP4 transcripts (blue puncta) and ADCY8 ( o ) or PFKP ( p ) transcripts (red puncta). Scale bars, 20 μm ( o and p ). Quantification (right) was performed using unpaired two-tailed Student’s t -tests ( ADCY8 : n  = 117 (non-AD) and n  = 76 (AD) cells; PFKP : n  = 43 (non-AD) and n  = 40 (AD) cells). The dots represent individual cells, pooled from eight samples (four individuals; each had one PFC and one thalamus sample). Activ., activation; DAM, disease associated microglia; ox. phos., oxidative phosphorylation; resp., response.

We next identified genes with higher differential effects in either NFTs or neuritic plaques (Fig. 4c , Extended Data Fig. 11c–f and Supplementary Table 10 ). Consistently, NFT-associated genes (374 genes, differentially expressed in 2+ cell types) included PLCG2 , CLU and CTNNA2 (in oligodendrocytes and OPCs) and mitochondrial subunits, and were enriched for ER protein processing, electron transport and cadherin binding (Fig. 4d,e ). Neuritic-plaque-associated genes (190 genes) included the energy-homeostasis-regulating genes IRS2 , PDK4 and HIF3A , and genes enriched for immune response, chromatin regulation and lipid droplets. Notably, in excitatory neurons, plaque-associated and upregulated DEGs were strongly enriched for aerobic transport chain components (including NDUFA4 and COX6B1 ) (Fig. 4f,g ). On the other hand, NFT-associated and downregulated DEGs were enriched for TCA cycle genes, whereas upregulated DEGs were enriched for unfolded protein response and lysosome-linked genes. Finally, astrocytes contained more plaque-associated DEGs compared with other cell types, and their pathology-associated DEGs were enriched in our expression modules, including in metallostasis (M28) for plaque-associated DEGs and oxidative phosphorylation (M27) and chaperones (M8) for NFT-associated DEGs (Fig. 4c,h–j ). Interestingly, a reactive astrocyte module (M3) was enriched in upregulated genes for plaques but in downregulated genes for NFTs (Fig. 4j ).

Given the enrichment of NFT-associated or plaque-associated DEGs in expression modules, we next examined whether gene modules were enriched for AD DEGs (for AD pathology or for AD diagnosis) (Fig. 4k , Extended Data Fig. 11g and Supplementary Fig. 42 ). The same modules enriched for pathology-associated astrocyte DEGs were also enriched for the full sets of DEGs, including metallostasis (M28) with neuritic plaque DEGs and oxidative phosphorylation (M27) with NFT DEGs (Fig. 4k ). Modules including ECM, adhesion and neurogenesis-related genes were much lower in AD (M1 and M11), while the modules for specific astrocyte subtypes (M7, DCLK1 + ; and M24, DPP10 + ) were enriched for upregulated DEGs (Fig. 4k ).

We independently identified modules for heat-shock chaperones, glycolysis and oxidative phosphorylation in multiple cell types, which were correlated across cell types and were enriched for upregulated DEGs (Fig. 4k , Extended Data Figs. 6a,b and 11g and Supplementary Fig. 42a,b ). The glycolysis modules were enriched among diffuse plaque DEGs in microglia and astrocytes and shared a set of genes that included canonical glycolysis genes ( PDK1/3/4 , PFKL/P , PKM and PGK1 ), anaerobic glycolysis enzymes ( TPI1 and LDHA ) and stress-induced genes ( EGLN1 , DDIT4 , VEGFA and BNIP3L ) (Fig. 4k–m and Extended Data Fig. 6a,b ). All glial types upregulated core glycolysis driver GAPDH and mitophagy-regulating BNIP3L in response to NFT burden and in individuals with cognitive impairment 59 (Fig. 4m ). In regions with high diffuse plaque, astrocytes upregulated glycolysis enzymes converting glucose-6-phosphate to pyruvate, while downregulating MPC1 , the mitochondrial pyruvate transporter 60 (Fig. 4n ). In parallel, astrocytes uniquely upregulated DDIT4 , PFKP and ADCY8 , along with genes that suppress fatty acid metabolism ( ANGPTL4 ) and promote lipid droplet storage of fatty acids ( HILPDA ), while microglia upregulated multiple glycogen-related genes ( GBE1 , UGP2 and PYGL ) 48 (Fig. 4m ).

To validate differential expression of ADCY8 and PFKP , we performed in situ hybridization (RNAscope) in AG tissue samples from patients with AD and control individuals without AD and found a significant increase in transcripts of both genes in AQP4 + astrocytes (Fig. 4o,p ). Finally, we noticed that the glycolysis pathway genes were maximally expressed at different points in global AD progression for each region (pathology diagnosis by ABC score) 29 , 30 . The pathway peaked very early in the EC (ABC score of 1, low levels of AD pathology), later in the HC and midtemporal cortex (intermediate levels), and very late in the PFC (high levels) (Supplementary Fig. 42c ), suggesting that the glial metabolic response to AD may not be coordinated globally.

Astrocytes and cognitive resilience

In addition to understanding cellular alterations associated with specific pathological measures in AD, we investigated what transcriptional changes are associated with cognitive resilience (CR) in AD, cases in which individuals with AD brain pathology display much less cognitive impairment than expected 3 , 25 , 26 , 27 . To identify potential molecular mediators that confer CR to AD pathology, we defined CR either categorically as the absence of cognitive impairment despite a pathologic diagnosis of AD (clinical diagnosis condition), or continuously, as the difference between observed cognition and the cognition expected on the basis of pathology level (Fig. 5a ). We computed both scores for CR based on global cognitive function and for cognitive decline resilience (CDR) based on the rate of change of global cognitive function over time, and used four different measures of AD pathology: global AD pathology, neuritic plaque burden, NFT burden and tangle density (Fig. 5a ).

figure 5

a , The concept of CR and CDR scores. Pathology measurements are used to predict global cognitive function, for CR scores, or rate of cognitive decline, for CDR scores. b , The number of significant DEGs in major cell types across nine measures of CR. c – h , Association of astrocyte CR genes with measures of CR (global AD pathology CR score ( c ), neuritic plaque burden CR score ( d ), NFT burden CR score ( e ), tangle density CR score ( f ), global cognitive (cogn.) function ( g ) and rate of change of global cognitive function ( h )) across six major cell types in the PFC (427 individuals, DEGs were computed using muscat). i , The association between the expression of CR genes in astrocytes across six brain regions and CR to global AD pathology (48 individuals; DEGs were computed using MAST). j – l , RNAscope validation of the differentially expressed astrocyte CR genes PNPLA6 ( j ), GPCPD1 ( k ) and CHDH ( l ) in the PFC of individuals with cognitive impairment (CI) relative to cognitively resilient (CR) individuals. Representative images (top) show AQP4 transcripts (red puncta) and CR gene transcripts (blue puncta). Scale bars, 20 μm ( j – l ). Quantification (bottom) was performed using unpaired two-tailed Student’s t -tests; P  = 0.0249 ( j ), P  = 0.0052 ( k ), P  = 0.0375 ( l ). Data are mean ± s.e.m. PNPLA6 : n  = 3 (CI) and n  = 4 (CR) individuals; GPCPD1 and CHDH : n  = 4 individuals per group. m , Schematic of choline metabolism and polyamine biosynthesis; significant astrocyte CR genes are highlighted.

We calculated DEGs for both CR and CDR in each major cell type in the PFC (snRNA-seq from 427 ROSMAP study participants) 27 . Astrocytes were the only cell type with a consistently high number of genes associated with CR across all of the measures tested (Fig. 5b ). To identify specific molecular pathways within astrocytes that may contribute to CR, we focused on genes that are consistently associated with multiple measures of CR in astrocytes (termed CR-associated genes). Several CR-associated genes, including GPX3 , HMGN2 , NQO1 and ODC1 (encoding a rate-limiting enzyme of polyamine biosynthesis), possess or promote antioxidant activities 61 , 62 , 63 , 64 , 65 , 66 (Fig. 5c–f and Supplementary Fig. 43a–d ). The expression of HMGN2 , NQO1 , ODC1 and GPX3 in astrocytes was also positively associated with cognitive function (Fig. 5g and Supplementary Fig. 43e ), and these genes exhibited the highest expression in astrocytes isolated from those individuals with the least cognitive decline over time (Fig. 5h and Supplementary Fig. 43f ). Analysis of bulk RNA-seq data from the ROSMAP cohorts ( n  = 638) confirmed a significant positive association between the expression level of HMGN2 , ODC1 and GPX3 and multiple measures of cognitive function and CR to AD pathology (Supplementary Fig. 44a–d ).

Furthermore, we noticed that several CR-associated genes within astrocytes encode enzymes that catalyse metabolic reactions that are involved in choline formation and breakdown. The expression of GPCPD1 , which encodes glycerophosphocholine phosphodiesterase 1, an enzyme that is critical for cleaving glycerophosphocholine (GPC) to produce choline, was positively associated with measures of CR in astrocytes (Fig. 5c–f and Supplementary Fig. 43a–d ). Conversely, PNPLA6 , which encodes a phospholipase that catalyses the hydrolysis of intracellular phosphatidylcholine, a major membrane lipid, generating GPC, and CHDH , which encodes choline dehydrogenase, an enzyme that catalyses the conversion of choline to betaine aldehyde, were both negatively associated with multiple measures of CR in astrocytes (Fig. 5c–f and Supplementary Fig. 43a–d ). Many of the CR-associated genes identified in PFC astrocytes were also associated with CR in astrocytes from other regions of the human brain (Fig. 5i and Supplementary Fig. 45 ), corroborating a link between astrocytes and CR beyond the PFC.

To validate the choline pathway genes PNPLA6 , GPCPD1 and CHDH , we selected PFC samples from individuals with high amyloid and tau pathology and compared transcript levels between individuals with intact cognition (that is, cognitively resilient) to those with cognitive impairment, and performed in situ hybridization (RNAscope) analysis of these genes with AQP4 as a marker for astrocytes. We found a significant decrease in PNPLA6 and CHDH transcripts and a significant increase in GPCPD1 transcripts in cognitively resilient individuals, in agreement with the differential expression results (Fig. 5j–l ). Notably, choline oxidation to betaine generates a labile methyl group that can be used for homocysteine remethylation, resulting in methionine formation, which is subsequently transformed into the universal methyl donor S -adenosylmethionine 67 . S -adenosylmethionine is involved in the biosynthesis of spermidine, linking choline metabolism and polyamine biosynthesis in astrocytes in CR to AD pathology (Fig. 5m ).

Here we present a transcriptomic atlas of the aged human brain—spanning six brain regions from 48 individuals with and without a diagnosis of AD—that we used to annotate regional cellular diversity, identify gene expression programs and differences in AD across cell types, and pinpoint region-specific cell populations that are vulnerable to AD. We provide an interactive website for exploring the atlas and these annotations, markers, functional modules and differences in AD at both the single-cell and pseudo-bulk levels ( http://compbio.mit.edu/ad_multiregion ).

By annotating neuronal and glial subtypes by brain region, we found significant compositional differences between regions, including a subtype of thalamic GABAergic neurons ( MEIS2 + FOXP2 + ) that is molecularly distinct from the canonical subclasses of inhibitory neurons in the neocortex. We used region-specific measurements of AD pathology to identify changes in gene expression associated with neurofibrillary tau tangle or amyloid-β plaque burden, including plaque-associated upregulation of metallostasis in astrocytes and of the electron-transport chain in excitatory neurons. We found that AD-risk genes were highly perturbed in AD—in particular for microglia, consistent with their enrichment for GWAS signal 68 —but few risk genes showed region-specific expression. To further examine the cellular and regional heterogeneity of the human brain, we developed a scalable method, scdemon, which uses sample decorrelation to annotate both ubiquitous and rare gene expression programs in each major cell type, and used annotated modules to identify functional programs associated with specific pathological variables, including a glycolysis- and energy-metabolism-linked program in glia 48 , 60 associated with diffuse plaque burden.

We identified five excitatory neuron subtypes that were reduced in patients with AD (vulnerable subtypes) in the early-affected EC and HC 1 , 17 , 18 , including EC layer II (L2), RORB -positive L5 ( AGBL1 + GPC5 + ) 19 and hippocampal CA1 subfield neurons 20 , 21 , 22 , 23 . Notably, vulnerable excitatory neurons shared expression of genes involved in Reelin signalling and heparan sulfate proteoglycan biosynthesis, both of which were also predictive of inhibitory neuron vulnerability to AD. Recent case studies have identified variants in RELN and APOE as potentially mediating CR to autosomal-dominant AD. Notably, the RELN variant enhanced its binding to glycosaminoglycans (GAGs) and NRP1 , and the APOE variant decreased binding to GAGs, potentially affecting their ability to compete for receptor binding 69 , 70 . Thus, our findings suggest a convergence of factors associated with cellular vulnerability in sporadic AD, and resilience to autosomal-dominant AD.

Finally, we analysed the transcriptomic correlates of cognition and pathology in AD, and identified a set of astrocyte genes linked to CR to AD pathology. Notably, these genes converged on the pathways of choline metabolism and polyamine biosynthesis. This finding aligns with studies showing benefits of dietary choline intake and supplementation on cognitive performance in human individuals and in animal models 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 . Similarly, dietary supplementation with the polyamine spermidine prolongs life span and health span in several animal models 66 , and spermidine has also been shown to enhance memory performance and counteract age-related cognitive decline 79 , 80 , 81 . Our findings support choline metabolism and polyamine synthesis as attractive targets for promoting CR in AD.

Our study has several limitations: isotropic fractionation and read depth cut-offs may bias cell recovery based on their nuclear content; nuclear RNA may not fully capture microglial states 82 or localized transcriptomic changes; and pathology burden is based on per-sample averages instead of on the spatial context of each cell. Additional individuals and data modalities will strengthen future analyses of region-specific alterations in AD, and spatial data may help to further separate pathology-associated changes.

Data reporting

No statistical methods were used to predetermine sample size. The experiments were not randomized and the investigators were not blinded to allocation during experiments and outcome assessment.

Sample selection from ROSMAP

We selected 48 individuals from ROSMAP, both ongoing longitudinal clinical–pathological cohort studies of ageing and dementia, in which all of the participants are brain donors. The studies include clinical data collected annually, detailed post-mortem pathological evaluations, and extensive genetic, epigenomic, transcriptomic, proteomic and metabolomic bulk-tissue profiling 28 . For the purpose of this study, individuals were selected based on the modified NIA-Reagan diagnosis of AD and the Braak stage score (Braak stages 0, 1 and 2, n  = 20; Braak stages 3 and 4, n  = 14; Braak stages 5 and 6, n  = 14), with 26 individuals having a positive pathologic diagnosis of AD and 22 individuals having a negative pathologic diagnosis of AD 83 . Details of the clinical and pathological data collection methods have been previously reported 2 , 5 , 6 , 28 , 84 . Individuals were balanced between sexes (male:female ratios 13:13 in AD, 11:11 in NoAD), matched for age (median, 86.6 years (AD) and 86.0 years (no AD)) and post-mortem interval (median, 5.9 h (AD) and 6.3 h (no AD)). Informed consent was obtained from each participant, and the Religious Orders Study and Rush Memory and Aging Project were each approved by an Institutional Review Board (IRB) of Rush University Medical Center. The participants also signed an Anatomic Gift Act, and a repository consent to allow their data to be repurposed.

Dissection criteria

All dissections were done on a bed of dry ice using either a fine-toothed razor saw (for cortical regions) or a jewellers saw with diamond wire (for subcortical regions). Region-specific descriptions are as follows. (1) AG: full thickness cortex from the AG (Brodmann area: BA 39/40); take from the first or second slab posterior to the end of the HC. Minimize white matter. (2) MT: full thickness cortex from the middle temporal gyrus (BA 22); take as close to the level of the anterior commissure as possible. Minimize white matter. (3) PFC: full thickness cortex from the frontal pole (BA 10); take from the lateral side of the first or second slab. Minimize white matter. (4) EC: full thickness cortex from the EC (BA 28); take at the level of the amygdala. Avoid amygdala. Minimize white matter. (5) Posterior HC: take from the last slab containing HC. If the last slab has less than 5 mm of HC, take from the next slab anterior. Collect a full cross section. (6) TH: take from the first slab with thalamus. Include the most medial aspect.

Isolation of nuclei from frozen post-mortem brain tissue

The protocol for the isolation of nuclei from frozen post-mortem brain tissue was adapted from a previous study 12 . All of the procedures were performed on ice or at 4 °C. In brief, post-mortem brain tissue was homogenized in 700 µl homogenization buffer (320 mM sucrose, 5 mM CaCl 2 , 3 mM Mg(CH 3 COO) 2 , 10 mM Tris HCl pH 7.8, 0.1 mM EDTA pH 8.0, 0.1% IGEPAL CA-630, 1 mM β-mercaptoethanol and 0.4 U µl −1 recombinant RNase inhibitor (Clontech)) using a Wheaton Dounce tissue grinder (15 strokes with the loose pestle). The homogenized tissue was then filtered through a 40 µm cell strainer, mixed with an equal volume of working solution (50% OptiPrep density gradient medium (Sigma-Aldrich), 5 mM CaCl 2 , 3 mM Mg(CH 3 COO) 2 , 10 mM Tris HCl pH 7.8, 0.1 mM EDTA pH 8.0 and 1 mM β-mercaptoethanol) and loaded on top of an OptiPrep density gradient (750 µl 30% OptiPrep solution (30% OptiPrep density gradient medium, 134 mM sucrose, 5 mM CaCl 2 , 3 mM Mg(CH 3 COO) 2 , 10 mM Tris HCl pH 7.8, 0.1 mM EDTA pH 8.0, 1 mM β-mercaptoethanol, 0.04% IGEPAL CA-630 and 0.17 U µl −1 recombinant RNase inhibitor)) on top of 300 µl 40% OptiPrep solution (40% OptiPrep density gradient medium, 96 mM sucrose, 5 mM CaCl 2 , 3 mM Mg(CH 3 COO) 2 , 10 mM Tris HCl pH 7.8, 0.1 mM EDTA pH 8.0, 1 mM β-mercaptoethanol, 0.03% IGEPAL CA-630 and 0.12 U µl −1 recombinant RNase inhibitor). The nuclei were separated by centrifugation (5 min, 10,000 g , 4 °C). A total of 100 µl of nuclei was collected from the 30%/40% interphase and washed with 1 ml of PBS containing 0.04% BSA. The nuclei were centrifuged at 300 g for 3 min (4 °C) and washed with 1 ml of PBS containing 0.04% BSA. The nuclei were then centrifuged at 300 g for 3 min (4 °C) and resuspended in 100 µl PBS containing 0.04% BSA. The nuclei were counted and diluted to a concentration of 1,000 nuclei per μl in PBS containing 0.04% BSA.

Droplet-based snRNA-seq

For droplet-based snRNA-seq, libraries were prepared using the Chromium Single Cell 3′ Reagent Kits v3 according to the manufacturer’s protocol (10x Genomics). The generated snRNA-seq libraries were sequenced using NextSeq 500/550 High Output v2 kits (150 cycles) or NovaSeq 6000 S2 reagent kits.

snRNA-seq processing, QC, and annotation

Snrna-seq data preprocessing.

Gene counts were obtained by aligning reads to the GRCh38 genome using Cell Ranger software (v.3.0.2) (10x Genomics) 85 . To account for unspliced nuclear transcripts, reads mapping to pre-mRNA were counted. After quantification of pre-mRNA using the Cell Ranger count pipeline, the Cell Ranger aggr pipeline was used to aggregate all libraries (without equalizing the read depth between groups) to generate a gene–count matrix. The Cell Ranger v.3.0 default parameters were used to call cell barcodes. We used SCANPY 86 to process and cluster the expression profiles and infer cell identities. We retained only protein-coding genes and filtered out cells with over 20% mitochondrial or 5% ribosomal RNA, leaving 1.47 million cells over 48 individuals and 283 samples across all regions. We further filtered the dataset to the top 5,000 most variable genes and used them to calculate the low dimensional embedding of the cells (UMAP) (default parameters, using 50 principal components and 15 nearest neighbours) and clusters using the Leiden clustering algorithm at a high resolution (15), giving 337 preliminary clusters 87 . We separately called doublets using DoubletFinder and flagged and removed clusters with strong doublet profiles and clusters showing strong individual-specific batch effects, leaving a final dataset of 1.35 million cells 88 .

Cell type annotations

For the UMAP visualization of individual major cell type classes (excitatory neurons, inhibitory neurons, astrocytes, oligodendrocytes, OPCs, immune cells), the SCTransform-based integration workflow of Seurat was used to align data from individual samples, using the default settings 89 , 90 . We selected the set of relevant principal components on the basis of Elbow plots. We annotated cell types using previously published marker genes and single-cell RNA-seq data 9 , 12 , 33 , 91 , 92 , 93 . To annotate cell types on the basis of previously published single-cell RNA-sequencing data (Allen Institute’s cell types database; https://portal.brain-map.org/atlases-and-data/rnaseq/human-multiple-cortical-areas-smart-seq ), we used three separate approaches. First, Spearman rank correlation coefficients between the average expression profiles of neuronal subpopulations previously defined by the Allen Brain Institute 33 and the neuronal subtypes identified in this study were computed using the cor function in R. Second, to project annotations of neuronal subpopulations previously defined by the Allen Brain Institute onto the neuronal cells analysed in this study, we followed the integration and label transfer workflow of Seurat 90 . Third, we determined cell type marker genes based on data published by the Allen Brain Institute 33 using the FindAllMarkers function from Seurat (Wilcoxon rank-sum test with Bonferroni correction for multiple testing; P adj  < 0.05) and computed module scores for each cell type marker gene set across all neuronal cells analysed in this study using the AddModuleScore function of Seurat. To further annotate cell types, we determined marker genes using the FindAllMarkers function from Seurat (Wilcoxon rank-sum test with Bonferroni correction for multiple testing; P adj  < 0.05). We tested only genes that were detected in a minimum of 25% of the cells within the cell type (min.pct = 0.25) and that showed, on average, at least a 0.25-fold difference (log-scale) between the cells of the cell type and all remaining cells (logfc.threshold = 0.25). Marker genes of the high-resolution cell types or states were determined separately for each major cell type class. We additionally compared the EC excitatory neuron subtypes to cell type annotations previously reported previously 94 , which were computed using ACTIONet 95 , and compared microglial markers to previously reported subtypes 96 , 97 .

Cell cycle scores and global properties of gene expression

G2/M and S phase cell cycle scores were determined using the function CellCycleScoring in Seurat. Histograms showing the distribution of the G2/M- and the S phase module scores in each major cell class were generated using Prism 9 software. The statistical analyses comparing the number of genes detected per cell and the number of unique transcripts (UMIs) detected per cell between cell types was performed using Prism 9 software.

Integration of external data sources

Single-cell transcriptomic data from the human dLGN 98 were obtained from the Allen Brain Institute ( https://portal.brain-map.org/atlases-and-data/rnaseq/comparative-lgn ). Single-cell transcriptomic data from multiple cortical areas and the hippocampal formation of the mouse brain 43 were obtained from the Allen Brain Institute ( https://portal.brain-map.org/atlases-and-data/rnaseq/mouse-whole-cortex-and-hippocampus-10x ). Single-cell transcriptomic data across nine regions in the adult mouse brain 39 were obtained from the McCarroll and Macosko Labs ( http://dropviz.org/ ). Single-cell transcriptomic data from the mouse nervous system 40 were obtained from the Linnarsson laboratory ( http://mousebrain.org/adolescent/downloads.html ). The external datasets and the human multiregion data presented in this study were integrated using the reciprocal PCA (RPCA) pipeline with the default parameters in Seurat ( https://satijalab.org/seurat/articles/integration_rpca.html ). The integration of single-cell data was performed separately for astrocytes, excitatory neurons and inhibitory neurons. For the integration of GABAergic neurons, the single-cell transcriptomic data from multiple cortical areas and the hippocampal formation of the mouse brain 43 were downsampled to 50,000 GABAergic neurons. For the integration of excitatory neurons, the human multiregion dataset was downsampled to 5,000 neurons per high-resolution cell type. The mouse cortical data 43 were downsampled to 50,000 excitatory neurons. The frontal cortex, posterior cortex, HC and thalamus data of the DropViz dataset were combined and downsampled to 50,000 neurons. Downsampling of the data was performed using the Seurat function subset with the default parameters. The comparison of microarray data from different human brain regions was performed using the Differential Search tool of the Allen Brain Atlas data portal ( https://human.brain-map.org/microarray/search ). The thalamus was selected as the target structure and compared to the cerebral cortex as the contrast structure. The differential search results including the fold change values and P values of the top 2,000 genes were downloaded from the data portal.

Gene expression and regulon modules

Gene expression modules using zca (scdemon framework).

We would like to find gene expression modules by calculating gene–gene correlations in single-cell data and using these to detect communities of similarly expressed genes. However, in single-cell data, which often contain an unbalanced composition of cell types, modules computed using this approach will be dominated by the most common cell type markers and pathways. Moreover, correlation values will often be inflated for pairs of sparsely expressed genes. We developed a method which accounts for these pitfalls to call multiresolution gene expression programs from single-cell data using an SVD-based approximation of zero-phase component analysis (ZCA) and gene sparsity-dependent thresholding 99 , 100 .

scdemon (single-cell decorrelated module networks) method

The preprocessing transformations alternately called decorrelation, whitening, or sphering, transform a matrix X with a matrix W such that the covariance of XW is the identity matrix 101 . In particular, ZCA is the transformation which maximizes the similarity of the transformed data to the original, which is achieved by setting W  =  C −1/2 , where C is the covariance of X .

In single-cell data, given a count matrix X with n cells (rows) and g genes (columns), we would like to perform ZCA decorrelation on the samples as a preprocessing step for calling modules. Computing and storing the n by n sample-wise covariance C n  =  XX T / g is prohibitively expensive for modern datasets (with n  > 1 × 10 6 ), even without centring X . Instead, we can analytically approximate the covariance with the SVD of X T  =  U n S n V n T as C n  ≈ ( U n S n V n T ) T ( U n S n V n T )/ g  =  V n S n 2 V n T / g and therefore C n −1/2  =  g 1/2 V n S n −1 V n T . The ZCA transformation can then be computed as X ZCA  =  C n −1/2 X  =  g 1/2 V n S n −1 V n T X before calculating the covariance of X ZCA for downstream analysis. While this approximation is already tractable for small single-cell datasets, we may not be able to compute the matrix multiplications or centred SVD for larger datasets. Here, we can use the SVD of X  =  USV T , which is commonly calculated in single-cell analyses, to approximate C n −1/2 as g 1/2 US −1 U T and X ZCA  =  g 1/2 US −1 U T X . From this, the non-centred covariance of X ZCA is C ZCA  =  X ZCA T X ZCA / n  =  g  × ( US −1 U T X ) T ( US −1 U T X )/ n . By substituting the SVD in for X , this reduces to C ZCA  =  g  ×  VV T / n , which is a simple and efficient approximation for very large single-cell data. As this approximation commonly drops out the largest identity program in the data due to the decorrelation approach, we allow computing C ZCA  =  g  ×  VS p V T / n , for any p , to tune the relative involvement of the larger eigenvalue components of the SVD.

To control for inflated correlation estimates in highly sparse genes, we bin the estimated correlations ( C ZCA ) for each pair of genes according to their sparsities (fraction of cells expressing the gene, binned on a log 10 scale). We calculate the mean and s.d. for each 2D bin and smooth the estimates by fitting bivariate splines to the binned statistics, weighted by the log number of examples in the bin. We use the smoothed estimates to z -score the correlation matrix ( C ZCA ), which we then threshold with a single z -score cut-off to create an adjacency matrix for a gene–gene graph. Graphs are laid out using the Fruchterman–Reingold algorithm and we remove connected components with fewer than four genes 102 . We then use the leidenalg package and the Leiden algorithm with an RBConfiguration vertex partition to cluster the graph into gene modules 87 . To robustly estimate modules for each set of cells in our analyses, we first performed a grid search for the optimal number of SVD components for cells of that type. We then computed the z -scored matrices for each of 10 bootstraps, selecting 90% of batches for each bootstrap and using only genes expressed in over 5% of cells in the full dataset for the cell type. We thresholded the average of the bootstrapped z -score estimates with z  = 4.5 to build a graph. To balance the contributions of modules across the compositional spectrum, we calculated and thresholded separate graphs for eigenvalue powers p  = 0, 0.25, 0.5, 0.75 and 1 and combined them using multigraph Leiden clustering to call modules with leiden resolution = 3. Although we identify smaller modules, here we only report modules with at least 10 genes. We also ran the modules method on three published datasets, for which we ran the method with the same parameters on each dataset ( k  = 100, z  = 4.5, resolution = 2.5), used genes with >5% sparsity for the COVID 103 and brain 16 datasets and genes with >10% sparsity for the Tabula Sapiens dataset 104 , and report modules with 10 genes or more.

Module enrichments, network and contour plots

Module enrichments for cell subtypes and brain regions were performed using the hypergeometric test by calculating whether cells with a module score above 1 s.d. from the mean score were significantly enriched in a specific subtype or region. For plotting scores against other modules, averaged modules scores to either the subtype by sample level (within the same major cell type) or at the sample level alone (across cell types) and calculated Pearson correlations and P values using the cor.test function of R. To create the module–module network across microglial and immune modules, we calculated module–module score Pearson correlations using the logged module scores at the aggregated subtype by sample level, using a one-sided test with P adj  < 0.01 as a cut-off 105 . To generate contour plots of module expression on a UMAP, we first smoothed cell-level expression on a 500 × 500 grid with a 2D Gaussian kernel (size = 25 × 25 and σ  = 1) and then plot contours for smoothed values (0.1 to 0.8).

Gene expression programs using cNMF

Gene expression programs underlying both cell type identity and cellular activities were determined according to the consensus NMF (cNMF) analysis pipeline established previously using the default parameters 34 . The number of components ( K ) to use for cNMF was determined on the basis of a diagnostic plot showing the stability of the solution and the Frobenius reconstruction error as a function of K . To reduce runtime and working memory requirements, the data were downsampled using the Seurat function subset with the default parameters. The data were downsampled to 200 cells per major cell type. For the cNMF analysis at the level of high-resolution cell types, the analysis was performed separately on excitatory neurons, inhibitory neurons and astrocytes. For these analyses, the data were downsampled to 2,000 cells per astrocyte subtype and 1,000 cells per excitatory and inhibitory neuron subtype. Statistical significance of the overlap between the top 200 genes of a gene expression program and cell type marker genes was computed using Fisher’s exact tests.

SCENIC analysis and computation of regulon module scores

The gene regulatory network analysis was performed using pySCENIC with the default parameters 35 . To reduce runtime and working memory requirements, the data were downsampled to 2,000 cells per major cell type. For the SCENIC analysis at the level of high-resolution cell types, the analysis was performed separately on excitatory neurons, inhibitory neurons and astrocytes and the data were downsampled to 1,000 cells per high-resolution cell type. To identify the top cell-type-specific regulons, we calculated regulon specificity scores as described by previously and ranked the regulons based on their regulon specificity score 106 . Finally, we calculated the activity of each regulon in each cell using the AddModuleScore function of Seurat. The calculation of regulon module scores for major cell types was performed on a random sample of 50% of the cells (676,537 cells). For the analysis at the level of high-resolution cell types, the regulon module scores were determined based on all the cells of a major cell type class. For the statistical analysis of differences in the activity of regulons between cell types, the average regulon module score per individual and major cell type or high-resolution cell type was computed, respectively. The statistical analyses comparing the regulon module score activity was performed using Prism 9 software.

Analysis of GABAergic and glutamatergic module scores

GABAergic and glutamatergic module scores across all neuronal cell types were determined on the basis of a set of GABAergic and glutamatergic neuron marker genes, respectively, using the AddModuleScore function of Seurat. The sets of GABAergic and glutamatergic neuron marker genes were determined based on the human multiple cortical areas SMART-seq dataset from the Allen Brain Institute ( https://portal.brain-map.org/atlases-and-data/rnaseq/human-multiple-cortical-areas-smart-seq ). We identified marker genes using the FindAllMarkers function from Seurat (Wilcoxon rank-sum test with Bonferroni correction for multiple testing; P adj  < 0.05). We tested only genes that were detected in a minimum of 25% of the cells within the cell type (min.pct = 0.25) and that showed, on average, at least a 0.25-fold difference (log-scale) between the cells of the cell class of interest and all remaining cells (logfc.threshold = 0.25). To quantify the intermediate character of thalamic excitatory and inhibitory neurons, we first computed the average GABAergic and glutamatergic module score values for each neuronal cell type and for each individual. We then used the resulting data to determine the first principal component (PC1) scores (the coordinates of the individual observations on the first principal component axis) using the princomp function in R. The ridgeline plot showing the distribution of PC1 score for each neuronal cell type was generated using the ggplot2 package in R. To determine the association between the average glutamatergic and the GABAergic module score across neuronal cell types, we performed a simple linear regression analysis using Prism 9 software.

Analysis of extratelencephalic projection neuron module scores

Marker genes significantly upregulated in extratelencephalic projection neurons (exc. L5 ET) compared with near-projecting excitatory neurons in layers 5 and 6 (exc. L5/6 NP) were determined using the FindAllMarkers function from Seurat (Wilcoxon rank-sum test with Bonferroni correction for multiple testing; P adj  < 0.05). We tested only genes that were detected in a minimum of 25% of the cells within the cell type (min.pct = 0.25) and that showed, on average, at least a 0.25-fold difference (log-scale) between exc. L5 ET cells and exc. L5/6 NP cells (logfc.threshold = 0.25). The exc. L5 ET module score was computed based on the identified marker genes using the AddModuleScore function of Seurat. To determine the exc. L5 ET module scores across excitatory and inhibitory neurons, cells were downsampled to 2,000 cells per high-resolution cell type.

Cell–cell communication analysis

Cell–cell communication events were predicted using the LIgand-receptor ANalysis frAmework (LIANA) 107 in R. Specifically, the ligand–receptor analysis was performed using liana_wrap(). The methods included were CellPhoneDB 108 , NATMI 109 and SingleCellSignalR 110 . liana_aggregate() with the argument ‘aggregate_how’ set to ‘magnitude’ was run to find consensus ranks of different methods. Only interactions (ligand–receptor pairs) with a robust rank aggregation (RRA) score smaller than 0.05 (aggregate_rank < 0.05) were considered in downstream analyses. The interaction score of ligand–receptor pairs was calculated by applying −log 10 transformation to the RRA score (aggregate_rank). To determine the number of interactions and the overlap of interactions between regions, liana_wrap() was run on the pool of cells isolated from all individuals, with separate analyses conducted for each brain region. To determine cell–cell communication events that are brain-region specific, liana_wrap() was run separately for each individual. We then used a linear mixed-effects model to evaluate the association between the interaction scores of individual ligand–receptor pairs obtained from LIANA and the respective brain region serving as the predictor variable. To account for potential confounding factors and individual variability, we included age, sex and post-mortem interval as covariates in the linear mixed-effects model. These variables were added as fixed effects to the model. Moreover, we included a random effect for the individual to capture the participant-specific variability in the data. Linear mixed-effects models were implemented using the R software packages lme4 111 and lmerTest 112 . The lmer() function from the lme4 package was employed to fit the models. To obtain P values for the fixed effects in these models, we used the lmerTest package, which incorporated Satterthwaite’s degrees of freedom approximation. To account for multiple hypothesis testing, the obtained P values were further adjusted using the Bonferroni method.

Cell type composition

Analysis of cell type composition differences between brain regions.

For comparing the relative abundance of major cell types across brain regions, the fraction of cells of a major cell type class was computed relative to all the cells isolated from a region. For the statistical analysis of cell type composition differences between brain regions, we also computed the relative abundance of major cell type classes separately for each study participant. To this end, the fraction of cells of a major cell type class was computed relative to all the cells isolated from a brain region of an individual. At the level of high-resolution cell types or cell states, two distinct measures of relative abundance were computed. First, the relative abundance of each subtype of a major cell class was computed as the proportion of a subtype relative to all cells of the corresponding major cell class isolated from a brain region. Second, for the statistical analysis of differences between brain regions, the fraction of cells of a subtype was computed relative to all the cells isolated from a brain region of an individual. The statistical analyses comparing the relative abundance of major cell types and subtypes between brain regions was performed using Prism 9 software.

Analysis of cell type composition alterations in AD

We calculated compositional differences in individuals with AD versus individuals without AD (or AD dementia versus no dementia) by modelling the number of cells of a certain cell type or subtype in a specific sample (individual by region) relative to the total number of cells using a quasi-binomial regression model. We modelled AD status by binary ascertainment variables (cogdx 4–5, NIA-Reagan score 1–2, Braak stage 5–6 versus others, as well as any detected presence of NFTs, neuritic plaque or diffuse plaques in the region) while adjusting for brain region and sex. We used the emmeans package in R to assess the significance of the regression contrasts and used p.adjust with the fdr method to adjust P values. We modelled the effects of fraction of cells on cognitive performance in multiple domains with gaussian linear regression of cognitive performance on last visit versus the log 10 -transformed fraction of cells in the subtype or major cell type jointly with covariates for age, sex, APOE-ε4 and post-mortem interval, with false-discovery rate P -value correction (p.adjust in R). We compared the fractional abundances of pairs of neuronal subtypes between two regions using Kendall’s τ only in individuals with AD (NIA-Reagan score). Significance was assessed using beta regression (R library betareg) controlling for sex, APOE genotype, post-mortem interval and age of death, and we adjusted P values using p.adjust in R with the fdr method.

Differential gene expression

We performed differential expression analyses with three separate methods: MAST, Nebula and Wilcoxon testing 113 , 114 . For all methods, we subset the tested genes to only genes present in over 20% of cells. For MAST and Nebula, we calculated and included in the regression the top 10 components of unwanted variation calculated using RUV on the pseudo-bulk-level data (individuals by regions). For these methods, we also included as covariates the individual’s sex, age of death and post-mortem interval, each cell’s counts per gene and number of captured genes and, where applicable, the high-resolution cell subtypes and the brain region. For Nebula we used a Poisson mixed-model on the counts data with an offset of the log 10 -transformed total counts per cell. For MAST and Wilcoxon, we normalized each cell to a total library size of 10,000 counts. We ran Wilcoxon tests on both the cell and individual levels. We adjusted P values for multiple testing in all cases by using the p.adjust function in R with the fdr method. For our final set of differential genes in each analysis, we took all genes that were significant ( P adj  > 0.05) and concordant in both the MAST and Nebula results. We also provide the results for Wilcoxon tests, but did not use these to determine concordant results as they do not correct for many covariates. We computed differential expression against five AD ascertainment variables: continuous measurements of NFT, plaq_n, and plaq_d measured in each region except the thalamus (excluded from these analyses) and binary cognitive impairment (cogdx no dementia = 1 and 2 versus AD dementia = 4 and 5) and NIA-Reagan score classifications (non-AD = 3 and 4 versus AD = 1 and 2). We provide differential expression results for each of the 14 major cell types (with T cells, CNS macrophages, and each vascular subtype separately) for all regions jointly and for each region separately. We also provide results for each of the excitatory subtypes either in its most prevalent region for EC, HC or TH subclasses, or across the neocortex for neocortical subtypes (Supplementary Table 9 ). We also computed DEGs for the interaction between pathologic diagnosis of AD and sex in each major cell type, both across all regions and in each region separately. For the glial energy metabolism analyses we recomputed all DEGs in glial glycolysis-associated modules separately (keeping all genes, with no cell percentage cut-off). Glycolysis pathway diagram is from the glycolysis and gluconeogenesis pathway from WikiPathways 115 .

Pathology-biased DEGs

Pathology-biased DEGs were based on neuritic plaque or NFT pathology measurements in each region and were computed in each major cell type across all regions and in each region (except for the TH). Genes were ordered by the residual between NFT effect size and predicted NFT effect size from a regression using plaque effect size and region. Genes were retained if they were consistently up (or down) in 3+ regions for either NFT or plaque but in fewer than 2 regions for the other pathology measurement (shared genes are genes found in 2+ cell types).

Comparison with published DEGs

We compared our differential expression results to results from seven different previously published studies 11 , 12 , 19 , 47 , 48 , 49 , 50 . We compared the published DEGs both to: (1) cross-region DEGs calculated in each major cell type for individual-level AD status (NIA-Reagan score or clinical diagnosis of AD) and for quantitative measurements of AD pathology (neuritic plaques, diffuse plaques and NFTs); and (2) region-specific DEGs calculated in each major cell type and in endothelial cells, computed relative to pathologic diagnosis of AD (NIA-Reagan score, AD, 1–2; non-AD, 3–4). As some studies reported only the significant genes, we compared the log-transformed fold change estimates for our DEGs and reported DEGs by a Pearson correlation test.

DEG module enrichments

To assess the enrichment of upregulated, downregulated non-differentially expressed genes in each module, we first assigned each tested DEGs to its closest module by correlation to the module’s average expression profile. We then performed a hypergeometric enrichment test for the number of genes in a category (upregulated, downregulated, not differentially expressed) assigned to the module, against the total number of tested genes assigned to the module, the total number in the category and the total number tested and corrected P  values using p.adjust (Benjamini–Hochberg). Enrichments of pathology-biased DEGs in modules were performed in the same manner.

Neuronal DEG partitions

To partition neuronal DEGs into non-vulnerable and vulnerable-associated subclasses, we calculated each genes’ average expressions and differential expression effect sizes at the subtype level and compared these to the relative depletion of the subtypes. For each gene that was differentially expressed in late-AD (stratified by Braak stage, late AD, 5–6 versus non-AD or early-AD, 1–4) in at least 25% of all neuronal subtypes, we calculated the correlation of its average subtype expression in late-AD with each subtype’s compositional stability (log 2 [OR] in late AD) across excitatory subtypes, separating non-vulnerable-associated genes (correlation > 0.2) from vulnerable-associated genes (correlation < −0.2). We calculated functional enrichments on neuronal DEG partitions using the top 250 genes ordered by effect size in each category. We further separated DEGs with higher effect sizes in vulnerable subtypes from those with similar effect sizes across all neuronal subtypes by calculating the correlation of their differential effect sizes in each subtype with that subtype’s depletion (log 2 [OR] in late AD). To perform enrichments along the continuum of genes associated with vulnerability to non-vulnerability, we kept only genes with biased effect sizes (effect size correlation < −0.2) and binned them along the axis of expression correlation (window size 0.2 for at 0.05 intervals) and performed functional enrichments for all bins jointly.

DEG and module pathway enrichments

We performed DEG enrichments for each differential expression run using the gprofiler2 package in R, with multi-query for upregulated and downregulated genes, as unordered queries, a P -value cutoff of 0.05, and using GO, REAC, WP, KEGG and CORUM as annotation sources, and retained enriched terms with fewer than 500 genes. Module and module cluster enrichments were performed in the same manner, using the core genes identified for each module and for genes found in more than two modules within a module cluster.

Markers of neuronal vulnerability

We identified markers associated with excitatory neuron subtype vulnerability by performing linear regression to predict the log 2 [OR] of each subtype’s depletion in late AD based on its expression at the subtype-aggregate level (log[ X  + 1], averaged normalized expression in each subtype by region by individual batch), controlling for age, sex and post-mortem interval and adjusting P values with p.adjust (fdr).

Identification of genes associated with cellular vulnerability in inhibitory neurons

Processed snRNA-seq data (DLPFC, experiment 2) were obtained from Synapse ( syn51123521 ) and integrated with our own PFC snRNA-seq dataset comprising 427 individuals. To identify vulnerable inhibitory neuron subtypes, we examined the association between the relative abundance of cell types and the measure of NFT density (variable tangles). We used a quasi-binomial regression model to model the number of cells belonging to a specific cell type in a given sample (individual study participant), relative to the total number of cells in that sample. We fitted the regression model using the glm function in R, including age, sex and post-mortem interval as covariates. P  values were corrected for multiple testing using the Benjamini–Hochberg procedure as implemented in the R function p.adjust. The results are presented in the form of association scores (signed −log 10 -transformed Benjamini–Hochberg-adjusted P value, where the sign was determined by the direction (positive or negative) of the association). Inhibitory neuron subtypes demonstrating a significant negative association with tangle density (Benjamini–Hochberg-adjusted P value < 0.05) were classified as vulnerable subtypes, while all other subtypes were categorized as non-vulnerable. Genes exhibiting differential expression between vulnerable and non-vulnerable inhibitory neuron subtypes were identified on the basis of our PFC snRNA-seq dataset. This analysis was restricted to individuals without a pathologic diagnosis of AD. The differential expression analysis comparing vulnerable to non-vulnerable inhibitory neuron subtypes was performed using the R package dreamlet ( https://diseaseneurogenomics.github.io/dreamlet/ ). We used the dreamletCompareClusters function with the argument ‘method’ set to ‘fixed’ for this analysis. Adjusted P values for multiple testing were obtained using the topTable function of dreamlet, with the ‘adjust.method’ set to ‘BH’.

GWAS analyses

Intersection of regional expression and pathology-specific DEGs (across all regions) was performed for 149 annotated AD GWAS familial and AD risk loci from recent GWAS 54 , 56 , 57 , 58 . We calculated the disease-relevance score of each cell in the dataset against a recent Alzheimer’s GWAS, using scDRS (based on MAGMA) 54 , 55 , 116 . For the scDRS results, we counted the fraction of cells with significant scDRS scores (FDR < 0.05) in each cell type, subtype and region. To test for overlap with microglia/immune modules, we compared the set of immune cells with significant expression of each module ( z score > 2.5) and with the set of cells with significant scDRS scores (FDR < 0.05) and performed a hypergeometric test for significance of the overlap ( P adj  < 0.01, Benjamini–Hochberg correction). To identify region-specific GWAS genes, we performed an analysis of variance for the effect of region on average gene expression at the pseudobulk level.

Identification of genes associated with CR

To quantify CR, we computed a CR score as the difference between the observed cognition and the cognition predicted by a linear regression model, given the level of pathology (Fig. 5a ). Using this approach, we computed cognitive resilience (CR) scores based on the measure of global cognitive function and CDR scores based on the measure estimating the rate of change of global cognitive function over time (Fig. 5a ). Four distinct CR and CDR scores were derived using four distinct measures of AD pathology, namely global AD pathology and, separately, neuritic plaque burden, NFT burden and tangle density.

We performed differential expression analyses using the R package muscat to identify genes associated with CR in the PFC 117 . Low-expressed genes were excluded and only genes with more than one count in at least ten cells were considered. To take advantage of robust bulk RNA-seq differential expression frameworks, such as edgeR 118 , in a first step, muscat aggregates measurements for each sample (in each cluster) to obtain pseudobulk data. Using this approach, single-cell measurements were aggregated per study participant and cell type using the sum of raw counts option. Differential expression analysis was run using the edgeR method as implemented in muscat. We included as covariates the individual’s age at death and post-mortem interval. We report adjusted P values for multiple testing in all cases by using the p.adjust function with the Benjamini–Hochberg method as implemented in muscat. The multiple testing correction was performed locally, that is, on each of the cell types separately with the number of tests equal to the number of genes considered. These differential expression analyses were performed on the entire set of 427 individuals except for the group-based differential expression analysis based on our categorical definition of CR. In this case, we focused on comparing two distinct groups determined by their pathologic and clinical diagnoses of AD. First, we identified individuals with a pathologic diagnosis of AD, using the NIA-Reagan pathology criteria. Subsequently, these individuals were further categorized on the basis of their clinical consensus diagnosis of cognitive status at the time of death. Specifically, we compared individuals with no cognitive impairment (NCI, final consensus cognitive diagnosis (cogdx) value of 1) against individuals with a cognitive diagnosis of AD dementia and no other cause of cognitive impairment (cogdx value of 4) among individuals with a pathologic diagnosis of AD.

To confirm the differential gene expression results based on the CR and CDR scores, we also evaluated the association between gene expression and global cognitive function or the rate of change of global cognitive function adjusting for AD pathology as a covariate. The AD pathology measures considered as a covariate were global AD pathology (gpath), neuritic plaque burden (plaq_n), NFT burden (nft), or tangle density (tangles). Thus, together with the DGE analysis based on CR and CDR scores, we performed a total of 16 different tests assessing the association between gene expression and CR.

We used the model-based analysis of single-cell transcriptomics (MAST) tool to investigate whether the CR genes identified in PFC astrocytes were also associated with CR in astrocytes from other regions of the human brain. To ensure robust analysis, we initially filtered the genes under investigation, selecting only those with more than one count in at least 10 cells. The analytical model incorporated the condition variable of interest, as well as several covariates known to influence gene expression. These covariates included the cellular detection rate (cngeneson), age at death (age_death), post-mortem interval (pmi), and sex (msex). We also accounted for potential participant-specific variation in the data by incorporating a random effect term for the individual (1|individual). To account for multiple comparisons, the P values were adjusted using the FDR method as implemented in the p.adjust function.

Bulk RNA-seq differential expression analysis

Differential expression analysis of bulk RNA-seq data from the ROSMAP cohorts was performed using DESeq2 119 (plotted) and edgeR 118 . Age at death and post-mortem interval were converted into z scores and included as covariates in the regression equation. Both approaches (DESeq2 and edgeR) provided similar results.

Permutation test for evaluating the significance of the overlap of DEGs between our dataset and the SEA-AD dataset

The average expression level of each gene within each major cell type was determined using the ‘AverageExpression’ function from the Seurat R package. The genes considered in the differential expression analysis for each major cell type were categorized into ten subsets based on their average expression level within the corresponding cell type. We next intersected the genes in each of the ten subsets with genes identified as significantly associated with either neuritic plaque burden (in our dataset) or the CPS score (in the MTG SEA-AD dataset). This intersection enabled us to determine the number of significant DEGs in each subset. The process was performed separately for genes positively and negatively associated with AD pathology. Subsequently, we randomly sampled the determined number of significant DEGs from each of the 10 subsets, ensuring that the expression level distribution of the DEGs was preserved in the random samples. This random sampling step was repeated for a total of 1,000 iterations. These steps were performed separately for both our dataset and the SEA-AD dataset. For each of the 1,000 random samples, we determined the overlap of genes between datasets and compared it to the observed overlap between the two datasets. To assess the significance of the observed overlap, we computed z scores, which represent the difference between the observed value of overlap and the mean value of overlap based on the permutation results, divided by the s.d. of the permutation results.

Comparison with previously published proteomics study of AD

To further validate our differential expression results, we evaluated the correlation between the effect sizes of gene expression changes observed in our study and those identified through quantitative proteomics 51 . We specifically examined the correlation between the effect sizes of genes associated with neuritic plaque burden in our study and the effect sizes of overlapping differentially expressed proteins in the quantitative proteomics analysis of bulk tissue. The correlation was computed using the cor.test function in R with the argument ‘alternative’ set to ‘two.sided’ and the argument ‘method’ set to ‘pearson’. P values were adjusted for multiple testing using the Benjamini–Hochberg method as implemented in the R function p.adjust.

Inter-regional comparison of AD pathology-associated gene sets in glial cells along the spectrum of global AD pathology burden

We determined genes significantly associated with global AD pathology for each glial cell type, using single-nucleus RNA sequencing data from the PFC of 427 participants in the ROSMAP study. We then calculated module scores for these gene sets in astrocytes, microglia, oligodendrocytes, and OPCs using the Seurat ‘AddModuleScore’ function. The module scores were determined separately for genes positively and negatively associated with global AD pathology. To assess the progression of these scores across the spectrum of global AD pathology burden, we averaged the module scores of all cells of a specified cell type isolated from the brain region of interest of an individual. For visualizing the relationship between the global AD pathology burden and mean module scores, we employed Locally Estimated Scatterplot Smoothing (LOESS) using the ggplot2 package in R, with the ‘geom_smooth’ function and the ‘method’ parameter set to ‘loess’. The correlation of mean module scores between regions was determined using the cor.mtest function of the R package corrplot. P values were adjusted for multiple hypotheses testing using the Benjamini–Hochberg method as implemented in the R function p.adjust.

In situ hybridization (RNAscope)

Frozen human post-mortem brain samples were embedded in Tissue-Tek OCT compound (VWR; 25608-930), sectioned on a Leica cryostat at a thickness of 20 μm, and mounted onto Fisherbrand Superfrost Plus microscope slides (Thermo Fisher Scientific; 12-550-15). Slides were fixed in 4% paraformaldehyde at 4 °C for 30 min, and dehydrated in ethanol. The RNAscope 2.5 HD Chromogenic Duplex Detection Kit and RNAscope Multiplex fluorescent V2 Kit (ACDBio) were then used according to the manufacturer’s instructions. Tissue samples were hybridized using the following chromogenic RNAscope probes: GAD2, FOXP2, MEIS2, AQP4, GRM3, ADCY8, PFKP, PNPLA6, GPCPD1 and CHDH (ACDBio). For in situ hybridization of Reelin, tissue samples were hybridized using the following fluorescent RNAscope probes: vGlut and Reelin. Cell nuclei were stained with 50% haematoxylin (for chromogenic experiments) or with Hoechst (for fluorescent experiments). For fluorescence RNAscope analysis, sections were incubated in TrueBlack (Biotium; 23007) for 10 s before Hoechst staining to quench auto-fluorescence. Images were acquired using the Zeiss LSM 900 confocal microscope, with a 63× oil objective. Two images were acquired per tissue sample. For both chromogenic and fluorescence RNAscope experiments, puncta were manually counted by researchers blinded to the experimental group of each image.

Immunohistochemistry

All experiments were performed according to the Guide for the Care and Use of Laboratory Animals and were approved by the National Institute of Health and the Committee on Animal Care at Massachusetts Institute of Technology. Sample sizes were determined on the basis of previous work from our laboratory, without power analysis calculation or randomization. In the experiment comparing App -KI (C57BL/6-App<tm3(NL-G-F)Tcs>, RBRC06344) and WT mice, the App -KI group consisted of 7 mice (5 male and 2 female) and the WT group included 6 female mice. In the experiment comparing Tau P301S (The Jackson Laboratory, 008169) to WT mice, both groups consisted entirely of male mice, with 6 mice in the Tau(P301S) group and 5 mice in the WT group. Mice were transcardially perfused with ice-cold phosphate-buffered saline, followed by 4% paraformaldehyde for fixation. Brains were dissected out and post-fixed in 4% paraformaldehyde overnight at 4 °C. Brains were sectioned horizontally on the Leica vibratome at a thickness of 40 μm. Slices containing the EC were selected under a dissecting microscope to ensure consistent anatomical structure across all cohorts. Brain sections were incubated in antigen retrieval solution (pH 6, 100 mM sodium citrate buffer, prewarmed to 80 °C) for 20 min, and then cooled to room temperature. The sections were then washed twice with phosphate-buffered saline, and blocked in buffer (0.3% Triton X-100, 2% bovine serum albumin, 10% normal donkey serum in phosphate-buffered saline) for 1 h at room temperature.

The sections were incubated in primary antibodies (anti-Reelin, 1:200; anti-NeuN, 1:200, anti-phospho tau, 1:200; and anti-amyloid-β, 1:500) overnight at 4 °C. After primary antibody incubation, the sections were washed three times with PBS, twice with blocking buffer and incubated in secondary antibody (1:1,000) for 2 h at room temperature. The sections were then washed three times with PBS, incubated with Hoechst (1:1,000) for 10 min and washed once more with PBS.

Confocal tile scans of the EC were acquired on the Zeiss LSM 900 using a 20× objective, with consistent laser setting across all cohorts. Layer II–III EC was identified based on previous criteria 120 . Orthogonal projections of the confocal tile scans were exported to Fiji for signal quantification. In Fiji, layer II–III of the EC was set as a region of interest, and a macro was used to count Reelin-positive cells in the region of interest and quantify the mean fluorescence intensity for each cell. The signal intensity of the Reelin channel was subsequently normalized to the NeuN signal. Researchers were blinded to animal genotype.

External data sources

Processed snRNA-seq data generated by the Seattle Alzheimer’s Disease Brain Cell Atlas (SEA-AD) consortium (SEAAD_MTG_RNAseq_final-nuclei.2023-05-05.h5ad) were obtained from the Seattle Alzheimer’s Disease Brain Cell Atlas (SEA-AD) ( https://sea-ad-single-cell-profiling.s3.amazonaws.com/index.html#MTG/RNAseq/ ). The SEA-AD DLPFC data (SEAAD_DLPFC_RNAseq_final-nuclei.2023-07-19.h5ad) were downloaded from https://sea-ad-single-cell-profiling.s3.amazonaws.com/index.html#DLPFC/RNAseq/ . Additional processed snRNA-seq datasets (specifically the h5ad files Neurons.h5ad and Nonneurons.h5ad) were obtained from the Linnarsson laboratory ( https://console.cloud.google.com/storage/browser/linnarsson-lab-human;tab=objects?authuser=0&prefix=&forceOnObjectsSortingFiltering=false ).

Reporting summary

Further information on research design is available in the  Nature Portfolio Reporting Summary linked to this article.

Data availability

snRNA-seq profiling data are available from Synapse in coordination with the ROSMAP project. Data are accessible under accession codes syn52293442 (as part of the MIT ROSMAP Single-Nucleus Multiomics Study; Synapse: syn52293417 ). The data are available under controlled use conditions set by human privacy regulations. To access the data, a data use agreement is needed. This registration is in place solely to ensure anonymity of the ROSMAP study participants. A data use agreement can be agreed with either Rush University Medical Center (RUMC) or with SAGE, who maintains Synapse, and can be downloaded from their websites ( https://www.radc.rush.edu/ ; https://adknowledgeportal.synapse.org/ ). Additional processed data as well as integrative visualization and exploration of the atlas are available online ( http://compbio.mit.edu/ad_multiregion/ and https://ad-multi-region.cells.ucsc.edu/ ) 121 . We also downloaded the following public single-cell gene expression datasets: human multiple cortical areas SMART-seq ( https://portal.brain-map.org/atlases-and-data/rnaseq/human-multiple-cortical-areas-smart-seq ), human DLPFC (Synapse: syn51123521 ), SEA-AD MTG ( https://sea-ad-single-cell-profiling.s3.amazonaws.com/index.html#MTG/RNAseq/ ), SEA-AD DLPFC ( https://sea-ad-single-cell-profiling.s3.amazonaws.com/index.html#DLPFC/RNAseq/ ), human dLGN ( https://portal.brain-map.org/atlases-and-data/rnaseq/comparative-lgn ), multiple human brain regions ( https://console.cloud.google.com/storage/browser/linnarsson-lab-human;tab=objects?authuser=0&prefix=&forceOnObjectsSortingFiltering=false ), multiple cortical areas and the hippocampal formation of the mouse brain ( https://portal.brain-map.org/atlases-and-data/rnaseq/mouse-whole-cortex-and-hippocampus-10x ), nine regions in the adult mouse brain ( http://dropviz.org/ ) and Mouse Brain Atlas ( http://mousebrain.org/ ).  Source data are provided with this paper.

Code availability

Code for analysis is available at GitHub ( https://github.com/cboix/admultiregion_analysis ) and Zenodo ( https://doi.org/10.5281/zenodo.11051020 ). The code for the scdemon method for module detection from single-cell RNA-seq is available at GitHub ( https://github.com/KellisLab/scdemon ).

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Acknowledgements

We thank the study participants and staff of the Rush Alzheimer’s Disease Center; all of the members of the Kellis and Tsai laboratories at MIT for discussions and feedback, including A. Grayson and P. Purcell for editing and feedback on the manuscript; the following members of the Mathys laboratory at the University of Pittsburgh for their assistance with the computational analysis: K. Ghafari, A. K. Kunisky, H. Zhao, S. Wang, J. I. Beaudway, E. Clark, Y. Ghaffari, W. R. Incorvaia, A. C. Laudenslager, V. N. Lohia and P. R. Patel; and M. Haeussler and B. Wick for their help in hosting the data on the UCSC browser. This work was supported in part by NIH grants RF1 AG062377, RF1 AG054321 and RO1 AG054012 (L.-H.T.), AG058002, AG062377, NS110453, NS115064, AG062335, AG074003, NS127187, MH119509 and HG008155 (M.K.) and the NIH training grant GM087237 (to C.A.B.). This work was partially supported by the Cure Alzheimer’s Fund, the JBP Foundation, the Robert A. and Renee E. Belfer Family Foundation, Eduardo Eurnekian and Joseph P. DiSabato. H.M. was supported by an Early Postdoc Mobility fellowship from the Swiss National Science Foundation (P2BSP3_151885). ROSMAP is supported by P30AG10161, P30AG72975, R01AG15819, R01AG17917. U01AG46152 and U01AG61356. ROSMAP resources can be requested at https://www.radc.rush.edu .

Author information

Present address: Department of Computer Science, Stanford University, Stanford, CA, USA

These authors contributed equally: Hansruedi Mathys, Carles A. Boix, Leyla Anne Akay

Authors and Affiliations

Picower Institute for Learning and Memory, MIT, Cambridge, MA, USA

Hansruedi Mathys, Leyla Anne Akay, Ziting Xia, Ayesha P. Ng, Xueqiao Jiang, Fabiola Galiana-Melendez, Kate Louderback & Li-Huei Tsai

Department of Brain and Cognitive Sciences, MIT, Cambridge, MA, USA

University of Pittsburgh Brain Institute, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA

Hansruedi Mathys, Ghada Abdelhady & Sudhagar Babu

Department of Neurobiology, University of Pittsburgh School of Medicine, Pittsburgh, PA, USA

Hansruedi Mathys

Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA, USA

Carles A. Boix, Kyriaki Galani, Julio Mantero, Neil Band, Benjamin T. James & Manolis Kellis

Broad Institute of MIT and Harvard, Cambridge, MA, USA

Carles A. Boix, Kyriaki Galani, Julio Mantero, Neil Band, Benjamin T. James, Li-Huei Tsai & Manolis Kellis

Computational and Systems Biology Program, MIT, Cambridge, MA, USA

Carles A. Boix

Harvard-MIT Health Sciences and Technology Program, MIT, Cambridge, MA, USA

Human Technopole, Milan, Italy

Jose Davila-Velderrain

Genetics and Aging Research Unit, McCance Center for Brain Health, Department of Neurology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA

Dmitry Prokopenko & Rudolph E. Tanzi

Rush Alzheimer’s Disease Center, Chicago, IL, USA

David A. Bennett

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Contributions

This study was designed by H.M., C.A.B., L.A.A., D.A.B., M.K. and L.-H.T., and directed and coordinated by M.K. and L.-H.T. The project was initiated by H.M. during his tenure as a postdoctoral associate in the laboratory of L.-H.T.; H.M., A.P.N., X.J., J.M. and K.G. performed sample preparations and single-cell RNA profiling. C.A.B. and H.M. led the computational analysis. L.A.A., Z.X., F.G.-M. and K.L. performed experimental validation experiments. G.A. and S.B. helped with the computational analysis. N.B., B.T.J. and J.D.V. contributed to computational method development and analysis. D.P. and R.E.T. contributed data for GWAS analysis. D.A.B. contributed samples and data. H.M., C.A.B., L.A.A., D.A.B., M.K. and L.-H.T. wrote the manuscript.

Corresponding authors

Correspondence to Li-Huei Tsai or Manolis Kellis .

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Extended data figures and tables

Extended data fig. 1 overview of the study sample and major cell type annotations..

a , Metadata overview: a total of 283 post-mortem brain tissue samples from 24 male and 24 female study participants were analysed across Alzheimer’s disease progression (AD). Top two panels show metadata at the individual level and bottom three panels show region-specific pathology measurements of neurofibrillary tangle burden (nft), neuritic plaque burden (plaq_n), and diffuse plaque burden (plaq_d). Individuals (columns) are ordered according to their global AD pathology burden. b , Joint UMAP of 1.3 M cells across 14 major cell types coloured and labelled by 76 high-resolution subtypes. c , d , Representation of individuals across cell types. The stacked bar plots show the proportion of cells contributed by each study participant across 14 major cell types ( c ) and 76 high-resolution cell types ( d ). e - f , Box plots of the number of genes detected per cell across all major cell types ( e ) and mean number of unique transcripts detected per cell per individual and major cell type across the six brain regions analysed ( f ). Within each box, horizontal lines denote median values; boxes extend from the 25th to the 75th percentile of each group’s distribution of values; whiskers extend from the 5th to the 95th percentile. ****P < 0.0001, ***P < 0.001, **P < 0.01; ns, P > 0.05; (ordinary one-way ANOVA corrected for multiple comparisons using Bonferroni’s multiple comparisons test). g , Relative abundance of inhibitory neurons originating from the medial (MGE) ganglionic eminences (SST and PVALB) and the caudal (CGE) ganglionic eminence (VIP, PAX6, and LAMP5) across brain regions. The bar plots show the mean fraction of cells per individual and brain region (AG, HC, MT, PFC: n = 48; TH: n = 45; EC: n = 46). The fraction of cells was computed relative to all the cells isolated from a brain region of an individual. Data are expressed as mean with 95% confidence intervals and individual data points are shown (two-way ANOVA corrected for multiple comparisons using Bonferroni’s multiple comparisons test).

Extended Data Fig. 2 Gene expression programs.

a , Heat map showing percent usage of all excitatory neuron gene expression programs (GEPs) (rows) in all excitatory neuron subtypes (columns). b , relative expression level of the top 20 genes associated with the gene expression program GEP Exc 15 (preferentially used by Exc NXPH1 RNF220 neurons) across all excitatory neuron subtypes. c , Heat map showing percent usage of all inhibitory neuron gene expression programs (GEPs) (rows) in all inhibitory neuron subtypes (columns). d , Expression level of the top 20 genes associated with the gene expression program GEP Inh 22 (preferentially used by Inh MEIS2 FOXP2 neurons) across all inhibitory neuron subtypes. e , Heat map showing percent usage of all astrocyte gene expression programs (GEPs) (rows) in all astrocyte subtypes (columns). f - h , Relative expression level of the top 10 genes associated with the gene expression programs GEP Ast 1 (preferentially used by the astrocyte subtype Ast GRM3) ( f ), GEP Ast 2 (preferentially used by the astrocyte subtype Ast DCLK1) ( g ), and GEP Ast 3 (preferentially used by the astrocyte subtype Ast LUZP2) ( h ) across all astrocyte subtypes.

Extended Data Fig. 3 Cell and subtype-specific transcription factor regulators.

a , Identification of major cell type-specific SCENIC transcription factor regulons. The heat map shows the module score of the top 5 transcription factor regulons (rows) for each major cell type across all individuals and major cell types (columns). b , Identification of inhibitory neuron subclass-specific SCENIC transcription factor regulons. The heat map shows the module score of the top 5 transcription factor regulons (rows) for each subclass across all individuals and subclasses of inhibitory neurons (columns). c , Identification of astrocyte subtype-specific SCENIC transcription factor regulons. The heat map shows the mean module score of the top 5 transcription factor regulons (rows) across all individuals and astrocyte subtypes (columns).

Extended Data Fig. 4 Region-specific cell-cell communication.

a - b , Ligand-receptor pairs with the greatest increase ( a ) or decrease ( b ) in interaction score in the thalamus compared to the prefrontal cortex. Bar plots show the interaction scores for the ligand-receptor pairs indicated. The interaction score was calculated by applying the minus log10 transformation to the robust rank aggregation (RRA) score. A lower RRA score indicates that a ligand-receptor interaction is ranked consistently higher than expected by chance across multiple prediction methods. Violin plots show the expression of the ligand (left) and receptor (right) in the cell types and brain regions indicated.

Extended Data Fig. 5 Module summary panels across modules.

a - h , Overview of gene expression modules with at least 10 genes each across all cells and across major cell types, showing the module name, number of genes, percent expression, top module genes, enrichments by subtype (except for neuron subtypes, see Supplement), covariates, and regions, and the top functional enrichment for each module. Percent expression is the percent of cells whose average expression (log1p, normalized) of the module is above 1. Covariate enrichments are performed by hypergeometric test, comparing the intersection of cells with z-scored module expression of at least 1 vs. with z < 1 against a particular level of a covariate of interest (e.g. cells from the entorhinal cortex region or cells of a specific subtype). Panels summarize modules found in all cells ( a ), astrocytes ( b ), OPCs ( c ), microglia and immune cells ( d ), oligodendrocytes ( e ), inhibitory neurons ( f ), vasculature and epithelia ( g ), and excitatory neurons ( h ). All modules except vasculature and epithelia modules are split into identity vs. other, where identity modules are highly enriched in a single subtype and have an average expression greater than 1 (log1p, normalized) for over 50% of the subtype’s cells.

Extended Data Fig. 6 Cross-module clustering and comparison.

a , Module-module correlation (Pearson correlation) and gene set overlap (Jaccard distance) for modules with at least 10 genes from all sets of modules (263 modules in total). Heatmaps are ordered by the hierarchical clustering of the correlation matrix and cuts represent 20 clusters cut from the hierarchical clustering dendrogram. Left and right side bars label rows by their modules set of origin (major cell type colours and grey for all cells). The most commonly shared genes in selected clusters of modules are shown on the right of the gene set overlap heatmap. b , Functional enrichments for each cluster of modules for the shared genes (>2 modules) in each cluster (only clusters with significant enrichments shown). Up to 5 enrichments shown, ordered by p-value, labelled by their source and only keeping terms with fewer than 500 genes. c , Covariate and functional enrichments for example astrocyte modules M19 (thalamus identity program) and M17 (cholesterol metabolism and biosynthesis program). Region, subtype, and covariate enrichments performed at cell level by stratifying cells with z-score > 1 and testing for regional or subtype enrichment (see  Methods ). Functional enrichments performed using gprofiler2, keeping terms with fewer than 500 genes. d , Scatterplots and correlation of scores for selected pairs of astrocyte modules. Each dot represents the module expression scores for a subtype in a specific sample and is coloured by the astrocyte subtype. Grey area represents the 95% confidence interval around the linear fit. e , Functional enrichments for selected astrocyte modules, showing top 10 functional enrichments for each pair of compared correlated modules (and for M6, M13, M27 together). Only terms with fewer than 500 genes shown. f , Microglial and immune modules network from correlation of module pairs at the subtype by sample level (edges shown where FDR-adjusted p-value < 0.05). Nodes are coloured by module’s relative expression in each of the microglial and immune subtypes and groups highlight sets of subtype-biased modules.

Extended Data Fig. 7 Neuronal vulnerability, connectivity, and markers of vulnerability.

a , Compositional differences for major cell types in AD by quasi-binomial regression with FDR-correction. log 2 OR shown both for each AD variable across regions (left) and for each region in late-AD (right). Analysis performed for individual-level AD status and region-level pathology measurements. Pathologic diagnosis of AD (Path. AD) was stratified by NIA-Reagan score (26 AD and 22 non-AD) and clinical diagnosis was stratified as AD dementia (n = 16) and non-CI (n = 32). b - c , Compositional differences for glial subtypes and inhibitory neuron subtypes according to individual-level AD status and region-level pathology measurements (as in a ). Grey boxes indicate interactions that are not computed due to MEIS2 FOXP2 specificity to the thalamus, where we do not have measured regional scores. d , Compositional differences in inhibitory neuron subtypes in late AD (Braak Stage 5-6 vs. 1–4) in each region. Grey boxes indicate interactions that are not computed due to subtype regional specificity. e , Boxplots (top) of neuronal fraction for two vulnerable EC subtypes, split by AD status (AD: blue, non-AD: red), with p-values from one-sided Wilcoxon test. Scatter plots (bottom) of individuals’ global cognition at last visit against cell fraction for two AD-vulnerable entorhinal cortex subtypes, coloured by AD. Linear fit with 95% confidence interval shown in grey. f , Estimated effect size of cell fraction (log 10 ) on scores for performance in various cognitive domains at last visit and combined scores from all domains (global). Linear regression FDR-corrected p-values (**adjusted p-value < 0.01, *<0.05, dot is <0.1). g , Full correlation matrix between subtype fraction between the hippocampus and entorhinal cortex in the same individuals, as described in the methods (***adjusted p-value < 0.001, **<0.01, *<0.05). i , Example genes predictive of subtype vulnerability. Scatterplots show average expression in the subtype across individuals against the effect size of the depletion or enrichment in AD as measured by the log 2 odds-ratio for late-AD, as in the Methods. i , Functional enrichments and intersected genes for top 30 markers of subtype vulnerability (terms with <500 genes). j , Association (quasi-binomial regression) between the relative abundance of inhibitory neuron subtypes in the prefrontal cortex and the density of neurofibrillary tangles. Association scores (signed negative log10 FDR-adjusted P value, where the sign was determined by the direction (positive or negative) of the association) are shown. The dotted line indicates the significance level threshold of an FDR-corrected P value of 0.05. P values were derived using the glm function in R and adjusted for multiple testing via the Benjamini-Hochberg method. k , Volcano plot showing genes differentially expressed in vulnerable versus non-vulnerable inhibitory neuron subtypes (genes significantly higher in vulnerable subtypes in red, lower in blue). FDR-adjusted P values as determined by the R package ‘dreamlet’ are shown. l , Scatter plot of each tested gene’s average differential expression effect size in late-AD (y-axis) versus the correlation of its expression in a subtype and that subtype’s level of depletion in late-AD (x-axis). Dashed lines separate genes associated with vulnerability and non-vulnerability. m , Functional enrichments for each identified class of neuronal DEGs (terms <500 genes) on bins (along x-axis from l ), from genes associated with vulnerability to those associated with non-vulnerability (only genes with biased effect sizes, see  Methods ). Dashed lines correspond to the same breaks as in ( l ).

Extended Data Fig. 8 Regional differential expression and GWAS association.

a , Number of up- and down-regulated differentially expressed genes (DEGs) with respect to pathologic diagnosis of AD for each major cell type, calculated in each region separately as well as jointly over all regions. b , Heatmaps of Jaccard similarity of DEGs across regions for each major cell type. c , Heatmap of -log 10 p-values for functional enrichments showing the top pathways for AD DEG shared across 3+ cell types. Enrichments shown for DEGs calculated in each region and in all regions together (up to the top 3 pathways per analysis are shown). d , Barplot of number of DEGs per region and cell type, coloured by type of DEG, as determined by its shared differential expression across regions and cell types. e , Top functional enrichments for region-specific DEGs and DEGs shared across regions (≥3 regions) with up to the top 2 terms (<500 genes only) shown per region. Panels shown and computed separately for each major cell type. f , Heatmap of log fold change for top shared, cell-type consistent, and cell+region-specific DEGs in major cell types. GG-NER: global genome nucleotide excision repair.

Extended Data Fig. 9 Inter-regional comparison of AD pathology-associated gene sets and region-specific GWAS enrichments.

a - b , Seurat module scores of genes significantly positively (top) or negatively (bottom) associated with the global AD pathology variable in prefrontal cortex for astrocytes, oligodendrocytes, OPCs, and microglia across brain regions and the spectrum of global AD pathology burden. The gene sets used for computing the module scores (genes significantly associated with global AD pathology burden) were determined based on snRNA-seq data derived from prefrontal cortex tissue of 427 ROSMAP study participants. The scatterplots ( a panels) illustrate the relationship between global AD pathology burden and the mean module score for the specified gene set, with this mean score calculated by averaging the module scores of all cells of the designated cell type isolated from an individual. A LOESS (Locally Estimated Scatterplot Smoothing) regression line with a 95% confidence interval is shown, and the regression lines are coloured by brain region. The central LOESS regression line represents the local measure of central tendency, calculated through locally weighted regression to reflect the smoothed relationship between the module scores indicated and global AD pathology burden. Interregional Pearson’s correlation analysis of mean module scores ( b panels) was performed by first averaging the module scores of all cells of the cell type of interest from an individual study participant. The correlation analysis was then performed between regions based on these averaged scores. P values were calculated using the cor.test function in R and were adjusted for multiple testing using the p.adjust function with the Benjamini-Hochberg method. c , Heatmap (by region, left) and barplot (over all regions, right) showing the percentage of cells with significant scDRS (disease relevance scores) for AD GWAS. Rows are split into major cell type groups (top) and microglia and immune subtypes. d , Regional expression (heatmap, left) and F-statistic for region in predicting expression (barplot, right) for eight GWAS genes with significantly region-specific expression in microglia. Barplot is coloured by the top expressed region (regression coefficient). Heatmap is labelled with stars if the gene is a DEG for that region. e , Boxplots showing expression of two of the region-specific GWAS genes in individuals with and without a pathologic diagnosis of AD. f , Microglia/immune modules associated with AD GWAS. Fraction of microglia or immune cells with significant expression of each module (z-score > 2.5) and with significant scDRS scores (FDR < 0.05). Only significant modules are shown (adjusted p < 0.01, hypergeometric test with BH correction).

Extended Data Fig. 10 Alzheimer’s disease GWAS-linked genes in the multi-region atlas.

a , Expression level by region/subtype and effect sizes of 150 Alzheimer’s disease candidate risk genes from Alzheimer’s disease GWAS risk loci. b , Differential effect sizes and significance for each candidate risk gene in each minor cell type across regional pathology measurements. Ependymal cells and CPEC cells were excluded as the thalamus does not have regional pathology measurements.

Extended Data Fig. 11 Pathology-biased DEGs for major cell types.

a , Number of DEGs for each cell type for both region-level pathology measurements and individual-level AD status (DE analysis performed over all regions jointly). b , Overlap of AD DEGs in each major cell type for each combination of region and condition (AD variable). DEG overlap computed by Jaccard distance and rows/columns hierarchically ordered by Euclidean distance. c - f , Scatter plots of average effect sizes for NFT and plaque for DEGs with biased differential effect sizes (left panels) and their respective functional enrichments (right panels), for DEGs specific to inhibitory neurons ( c ), oligodendrocytes ( d ), microglia ( e ), and OPCs ( f ). Genes are coloured by whether they have higher effect size relative to NFT (orange) or plaque levels (teal). g , Heatmap of hypergeometric enrichments of up (red) or down (blue) AD DEGs in modules for DEGs in all sets of modules across all regions, by AD condition. Only modules with at least two significant enrichments are shown and rows are clustered hierarchically by Euclidean distance.

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Mathys, H., Boix, C.A., Akay, L.A. et al. Single-cell multiregion dissection of Alzheimer’s disease. Nature (2024). https://doi.org/10.1038/s41586-024-07606-7

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Hydra for 21st century—a fine model in freshwater research.

two tailed hypothesis in research

1. Introduction

2. hydra : a model organism for biological and ecological research, 3. hydra in morphological studies, 4. hydra as a model organism in ecotoxicological research, 5. hydra as a test organism for more successful environmental decision-making, 6. hydra as a holobiont, 7. hydra in tumorigenesis research, 8. conclusions, author contributions, data availability statement, conflicts of interest.

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Kovačević, G.; Korać, P.; Želježić, D.; Sertić Perić, M.; Peharec Štefanić, P.; Sirovina, D.; Novosel, M.; Gottstein, S. Hydra for 21st Century—A Fine Model in Freshwater Research. Water 2024 , 16 , 2114. https://doi.org/10.3390/w16152114

Kovačević G, Korać P, Želježić D, Sertić Perić M, Peharec Štefanić P, Sirovina D, Novosel M, Gottstein S. Hydra for 21st Century—A Fine Model in Freshwater Research. Water . 2024; 16(15):2114. https://doi.org/10.3390/w16152114

Kovačević, Goran, Petra Korać, Davor Želježić, Mirela Sertić Perić, Petra Peharec Štefanić, Damir Sirovina, Maja Novosel, and Sanja Gottstein. 2024. " Hydra for 21st Century—A Fine Model in Freshwater Research" Water 16, no. 15: 2114. https://doi.org/10.3390/w16152114

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REVIEW article

Is it premature to formulate recommendations for policy and practice, based on culture and health research a robust critique of the cultureforhealth (2022) report.

\r\nMette Kaasgaard,

  • 1 Pulmonary Research Unit (PLUZ), Department of Medicine, Zealand University Hospital, Naestved, Denmark
  • 2 Department of Regional Health Research, Faculty of Health Sciences, University of Southern Denmark, Odense, Denmark
  • 3 Interuniversity Organisation Science and Art, Paris Lodron University Salzburg, Mozarteum University Salzburg, Salzburg, Austria
  • 4 Department of Art History, Musicology and Dance Studies, Paris Lodron University Salzburg, Salzburg, Austria
  • 5 Centre for Arts, Mental Health and Wellbeing, School of Allied Health and School of Humanities, The University of Western Australia, Perth, WA, Australia
  • 6 Institute for Creative and Cultural Entrepreneurship (ICCE), Goldsmiths, University of London, London, United Kingdom
  • 7 Music and Health Research Institute (MHRI), University of Ottawa, Ottawa, ON, Canada
  • 8 Department of Human Genetics, Hannover Medical School, Hanover, Germany
  • 9 Prince of Wales Clinical School, University of New South Wales, Kensington, NSW, Australia
  • 10 Sidney De Haan Research Centre for Arts and Health, Canterbury Christ Church University, Canterbury, United Kingdom
  • 11 International Centre for Community Music, York St John University, York, United Kingdom

Introduction: Arts and health practice and research has expanded rapidly since the turn of the millennium. A World Health Organization scoping review of a large body of evidence claims positive health benefits from arts participation and makes recommendations for policy and implementation of arts for health initiatives. A more recent scoping review (CultureForHealth) also claims that current evidence is sufficient to form recommendations for policy and practice. However, scoping reviews of arts and health research—without critical appraisal of included studies—do not provide a sound basis for recommendations on the wider implantation of healthcare interventions.

Methods: We performed a detailed assessment of 18 Randomised Controlled Trials (RCTs) on arts-based interventions included in Section 1 of the CultureForHealth report using the Joanna Briggs Institute Critical Appraisal Tool for RCTs (2023).

Results: The 18 RCTs included demonstrated considerable risks of bias regarding internal and statistical conclusion validity. Moreover, the trials are substantially heterogeneous with respect to settings, health-issues, interventions, and outcomes, which limits their external validity, reliability, and generalisability.

Conclusions: The absence of a critical appraisal of studies included in the CultureForHealth report leads to an overinterpretation and overstatement of the health outcomes of arts-based interventions. As such, the CultureForHealth review is not a suitable foundation for policy recommendations, nor for formulating guidance on implementation of arts-based interventions for health.

The CultureForHealth report ( 1 ) maps the literature in the field of culture, well-being and health in order to inform policy recommendations for Europe. The scoping review methodology employed did not include critical screening of the research studies included. In this paper, we report a critical assessment of 18 randomised controlled trials (RCTs) cited in Section 1 on “Culture and Health” of the CultureForHealth report using the Joanna Briggs Institute (JBI) Critical Appraisal Tool for RCTs (2023). The appraisals reveal considerable risks of bias across all trials, which limit their internal and statistical conclusion validity. The absence of a critical appraisal of studies included in the CultureForHealth report leads to an overinterpretation and overstatement of the health outcomes of arts-based interventions. As such, the CultureForHealth review is not a suitable foundation for policy recommendations, nor for formulating guidance on implementation of arts-based interventions for health.

Introduction

Since the turn of the millennium, there has been increasing attention internationally towards the potential wellbeing and health benefits of engagement with culture and creative arts activities. This interest has been motivated by the perceived need to draw on community assets outside the traditional medical field to address growing challenges in population health and demands made on healthcare systems due to funding constraints. Moreover, there is increasing recognition that medical science may face limitations in dealing with progressive long-term conditions and health inequalities and that greater efforts are needed to address social determinants of health across the life course ( 2 ). Thus, engagement with culture and creative arts are suggested as potential resources to support health through prevention, promotion, care, and treatment ( 3 ).

Efforts have been made to review the growing international body of research on culture, arts, and health in scoping and narrative evidence reviews, notably, by the All-Party Parliamentary Group for Arts, Wellbeing and Health, UK (2017, 2023) ( 4 , 5 ) and in reports reviewing evidence, e.g., from Europe ( 5 – 10 ), the US ( 11 ), and Australia ( 12 ). One considerable boost to further developments in the field has been given by a scoping review published by the World Health Organization (WHO) in 2019, summarising findings from over 3,000 studies ( 13 ). In addition, the WHO has supported the establishment of collaborating centres for arts and health research at University College London (UCL), and additional centres in the Steinhardt School at New York University and Edgehill University (UK). In 2023, the WHO and the Jameel Arts & Health Lab (New York, USA) announced a special Lancet Global Series on the health benefits of the arts ( 14 – 16 ) which “will show the scientific basis of the arts' role in health with rigour, and help position artists and scientists as necessary partners towards health and wellbeing for all” ( 16 ).

In 2022, Culture Action Europe ( 17 ) published a further scoping review - the CultureForHealth report ( 1 ) — to support: “Bottom-Up Policy Development for Culture & Wellbeing in the EU” ( 17 ). The report aimed “to synthesise existing evidence on the positive effect of arts and cultural activities on health and wellbeing” ( 17 ) and “to inform policy recommendations for Europe” (p. 24) ( 1 ). Studies published between 2005 and November 2021 were identified for the review following a search strategy using PubMed, Scopus, and other sources (see p. 26). The authors of the CultureForHealth report acknowledge limitations with their search strategy and that “our search terms may not have covered all possible valuable aspects of our focus theme very accurately” (p. 25). Section 1 of four sections in the report focuses on health benefits from cultural and arts participation and includes details of 137 empirical studies (including controlled trials and quasi-experimental, observational, qualitative, and mixed methods studies) and reviews (including systematic, scoping, and narrative reviews). Sections 2 to 4 are concerned with culture and subjective wellbeing, community wellbeing, and COVID-19, and are not considered in this paper.

The CultureForHealth report also includes a large section describing key challenges to public health across Europe and the authors state (p. 5) ( 1 ) that culture could help to effectively tackle these challenges:

1. The need for an increased focus on health promotion and disease prevention.

2. A growing mental health crisis.

3. The need to support the broader health and wellbeing of young people.

4. Ongoing changes to the labour markets, patterns of work and the economy.

5. An ageing population.

6. The association between ill health and patterns of inequality.

7. The need to promote active citizenship.

8. The mental health challenges faced by forcibly displaced people.

The findings and emerging initiatives associated with the CultureForHealth project have been showcased at various events (see weblinks in the Appendix p. 2), a guide tailored for practitioners has been published ( 18 ), and several activities are already in the process of implementation (see weblinks in the Appendix p. 1).

The WHO and the CultureForHealth scoping reviews, and other reports, do summarise a large body of empirical evidence on the benefits of arts initiatives, especially music and dance. However, scoping reviews alone are generally not a satisfactory basis for recommending healthcare interventions ( 19 – 21 ). Accordingly, serious concerns have been raised regarding the limitations of the WHO report ( 22 , 23 ) for its lack of critical appraisal of the studies included and for its willingness to take conclusions drawn in primary research studies at face value. Further critical papers have stressed the need for treating findings and conclusions from research and evidence reviews within arts and health with considerable caution until strong evidence has been established ( 22 , 24 – 28 ).

In this paper, we present the results of a critical appraisal of RCTs included in Section 1 in the CultureForHealth report. We focus on RCTs as these are widely regarded as providing the most robust source of evidence on effects of interventions on health outcomes and are, moreover, central to systematic critical reviews and acknowledged frameworks for clinical guidelines for safe, effective, and evidence-based healthcare interventions ( 29 – 33 ). In addition, we analyse the impact of this appraisal on the validity of the report conclusions and policy recommendations.

Inclusion and analysis procedure

Between February and April 2023, we identified all RCTs on arts/cultural interventions included in Section 1 of the CultureForHealth report ( 1 ). Table 2 in the report lists 20 RCTs, but one of the sources identified as such is not a randomised trial, and a second is not a trial report. This leaves 18 trials and data extraction was undertaken to describe characteristics of these RCTs. The RCTs were concerned primarily with singing, dance, and music listening interventions. We then undertook an appraisal of the RCTs using the revised JBI tool to assess risk of bias in RCTs ( 34 ) with respect to internal and statistical conclusion validity. The tool consists of thirteen questions with associated guidance (see Table 1 ), based on the Joanna Briggs Critical Appraisal Tool for the Assessment of Risk of Bias for Randomised Controlled Trials ( 34 ).

www.frontiersin.org

Table 1 . JBI critical appraisal tool for the assessment of risk of bias for RCTs ( 34 ): questions and guidance.

To ensure accurate appraisals, a two-stage strategy was employed:

Stage 1: Between July 2023 and November 2023, each trial report was appraised independently by two members of the research team for each domain (singing: MK, SC; dance: KG-H, SC; music listening and games: JS, SE). The assessors then met online and discussed their ratings and, where differences of opinion had arisen, an agreed judgment was reached through discussion and re-reading of the papers. Where two team members did not resolve differences, another member of the team was involved as moderator (JMM).

Stage 2: In addition, in December 2023, all papers were read again and appraised against each JBI question ( 34 ) by a single team member (SC), based on appropriate data extraction from all papers ( Supplementary Table 1 ). This helped to ensure that a reasonable relativity in judgement could be achieved, as assessments were made against the same standards. These judgements were then independently scrutinised by two other team members (MK, KHG) and any difference of opinion discussed and resolved. Findings from the second strategy were then used to moderate agreed ratings arising from the first strategy.

Characteristics of the RCTs

Section 1 of the CultureForHealth report includes reference to 18 RCTs (see Table 2 ). The art-form investigated varied: nine of the 18 trials were on group singing ( 35 – 43 ); five trials examined group dancing ( 44 – 48 ); three trials involved a musical intervention ( 49 – 51 ); and the final trial examined effects of games and painting ( 52 ). Moreover, the control arm(s) varied substantially from other arts-/culture-based activities to no intervention, or usual care (standard, health-care-based treatment).

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Table 2 . Characteristics of the 18 RCTs cited in Section 1 of the CultureForHealth Report ( 1 ).

The trials were conducted in 12 different countries: UK: 3 ( 35 , 37 , 41 ), China: 3 ( 40 , 50 , 51 ), Greece: 2 ( 46 , 47 ), the USA: 2 ( 45 , 48 ), and one each in Brazil ( 36 ), France ( 42 ), Germany ( 43 ), Iran ( 52 ), Italy ( 49 ), Portugal ( 44 ), Singapore ( 38 ), and Switzerland ( 39 ), i.e., only nine trials were conducted within the European Union. There was substantial heterogeneity regarding study durations, settings, health issues, participants, and outcome measure, and the RCTs varied considerably in size [smallest study ( 41 ): eighteen participants; largest ( 35 ): 258 participants]. Only five trials reported a prospective power calculation with target sample sizes achieved. The rest were either under-powered or did not report a prospective power calculation. In addition, nine trials were explicitly described as pilot studies ( 35 , 39 , 41 , 48 ), as a “pioneer” study ( 36 ), or as “exploratory” studies ( 37 , 40 , 43 , 46 ). Only three trials ( 35 , 39 , 41 ) reported on achievement of minimal clinically important differences (MCID) related to study outcomes and study findings observed.

Pre-registration, ethics, and CONSORT

Eleven trials provide details of pre-registration, including the trials' register number, so that the protocol is accessible. However, for seven trials, there is no indication that the study was pre-registered. These include two trials conducted in China ( 40 , 51 ), both studies in Greece ( 46 , 47 ), one in the USA ( 48 ), and those in Italy ( 49 ) and Portugal ( 44 ). All trials apart from one ( 51 ) report ethical approval, however, only seven provide an ethics committee reference number. All reports indicate that participants gave informed consent. Seven make explicit reference to CONSORT guidelines ( 53 ) and report a standard CONSORT flow diagram. However, only one includes a CONSORT checklist ( 39 ). Two trials refer to CONSORT guidelines, but the flow diagram is either incomplete ( 46 ) or is non-standard ( 43 ). Five trial reports ( 40 , 42 , 48 , 50 , 52 ) do not explicitly refer to CONSORT but do include a participant flow chart ( 42 , 44 , 47 , 50 , 52 ). Finally, two reports ( 46 , 51 ) make no reference to CONSORT and do not include any participant flow diagram.

Notably, authors in all trial reports acknowledge substantial limitations to their study and recommend further research with the conduct of large-scale trials.

Assessment of the 18 RCTs using the JBI Critical Appraisal Tool (2023)

Table 3 reports the consensus JBI tool ( 34 ) assessments of each of the 18 RCTs. Supplementary Table 1 provides example quotations from the trial reports to clarify the variations in ratings of the RCTs for questions in the JBI tool.

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Table 3 . Assessments of 18 RCTs cited in Section 1 of the CultureForHealth Report ( 1 ) using the JBI assessment tool ( 34 ).

JBI questions with high ratings

Table 3 shows that all trials were rated positively with respect to three questions: Q6: in all trials, treatment groups were treated identically apart from the intervention(s) of interest; Q8: in all trials, outcomes were measured in the same way; and Q13: for all trials, a standard and appropriate parallel groups design was employed. In two cases, however, the trials involved three arms [Fancourt and Perkins ( 37 )—intervention, active control and treatment as usual; Qin ( 51 )—music listening, painting and usual treatment]. All other trials involved two-arm intervention-control designs.

JBI questions with low ratings

All trials were rated as being at high risk of bias for two criteria: Q4: for all trials, participants were not blinded to the conditions they were allocated to, and Q5: for all trials, deliverers of interventions were not blinded to the activity (e.g., singing or dancing).

JBI questions with varied ratings

For the remaining questions in the JBI tool, assessments varied:

Q1: Seven trials ( 35 , 38 , 39 , 41 , 44 , 46 , 48 , 50 ) provide sufficient information that a satisfactory randomisation procedure was followed. In the remainder, we judged this to be unclear. Given, however, that all studies are described as RCTs, it was not possible to conclude that true randomisation did not take place for any study.

Q2: Concealment was judged to have taken place where a satisfactory randomisation process was described. Otherwise, concealment was unclear in most cases. For two trials, however, the authors explicitly state that concealment of allocation from researchers did not happen ( 37 , 43 ).

Q3: For 12 trials, trial groups appeared to be equivalent at baseline, with no significant differences on any outcome measure reported. For five trials, however, especially where sample sizes were small, marked differences in outcome means were apparent, even though these were reported as not statistically significant.

Q7: On the blinding of outcome assessors, Yes/No ratings were given for 11 of the 18 trials because multiple outcomes were assessed. Where the outcomes were objective assessments (e.g., lung function, cognitive function), the assessors were blinded. However, where outcomes were participant reported (e.g., quality of life, ratings of risk of developing depression), the assessments were not blind. For six trials, single or multiple outcomes were patient reported and so “No” rating is given on blinding of assessment at study level. In only two trials ( 49 , 52 ) were outcome assessments satisfactorily blinded.

Q9: In two trials ( 49 , 52 ), information was provided on the reliability of the data reported. These are both studies of children undergoing medical procedures where an observer assessed their levels of anxiety/fear. For a further study ( 44 ), reliability estimates for one of the outcomes assessed was presented but not for all of them. In all other trials, there is no direct evidence that the data reported was reliable. In most cases, however, it is clear that previously validated assessment procedures or questionnaires and scales were employed.

Q10: For 14 of the 18 trials, follow-up of participants throughout the trial was complete with very little or no attrition. For four trials ( 35 , 36 , 46 , 48 ), however, attrition was 15% or greater, and so judged as substantial.

Q11: In most trials, participants were judged to have been analysed as initially randomised, either because an intention-to-treat analysis was explicitly undertaken, or because there was little or no attrition in the course of the study. For three studies ( 36 , 46 , 48 ), however, this was not the case.

Q12: For five trials ( 35 , 39 , 42 , 45 , 49 ), the statistical analysis reported was judged to be appropriate. For a further four trials, the appropriateness of the analysis was judged to be unclear. For the remaining trials, we had substantial reservations regarding the analysis undertaken, which compromise the statistical conclusion validity of the study. These concerns are elaborated in the Discussion section below.

In the present study, we undertook a critical appraisal of the 18 RCTs included in Section 1 of the CultureForHealth report ( 1 ), which the authors of the report had not carried out. We analysed the basic characteristics and assessed risks of bias, using the JBI appraisal tool ( 34 ). The RCTs were characterised by substantial heterogeneity and high risks of bias, affecting both internal and external validity, and, hence, compromising the claims and recommendations stated within the CultureForHealth report.

Characteristics of the included RCT

There are key challenges with the basic conduct and reporting of many of the trials included in the CultureForHealth report. Firstly, approximately half of the trials had not been pre-registered, some did not conform to CONSORT guidance, and one trial failed to report ethical approval. These considerations alone should have resulted in extreme caution in even including these trials for consideration in a review. Secondly, the RCTs are characterised by high study heterogeneity regarding all aspects, as highlighted in Table 2 . Thirdly, given that the outcomes assessed are mostly based on patient-reported outcomes, the clinical relevance of findings reported is not always clear, with no reference to established cut-off values or MCID. Additionally, distinguishing between primary and secondary outcomes is often not clear. Fourthly, many trials are extremely small and under-powered, and, furthermore, involve predominantly females, so the extent to which the findings could be generalised even to males is questionable. Finally, descriptions of the arts-based interventions used are frequently lacking, including any disease-specific adaptions of the intervention, besides a frequent absence of appropriate and validated checklists for reporting within research on healthcare interventions [e.g., CONSORT ( 53 )].

These challenges severely limit both study replication to confirm or disconfirm findings and the reliable translation of a particular intervention to clinical and/or public health settings. Notably, nine trials are explicitly described as being a “pilot”, “pioneer”, or “exploratory”. As such, our analysis demonstrates that before even considering the assessments of the trials using the JBI tool, there are aspects of the trials which immediately raise questions over external validity and generalisability.

JBI appraisals of the RCTs

There are several issues affecting all or most of the trials which potentially introduce substantial risks of bias with respect to the outcomes. In all cases, both participants in interventions and those facilitating them were not blinded. This is unavoidable for arts-based activities of all kinds, but nevertheless, awareness introduces the potential for expectation and social desirability biases ( 54 , 55 ). A further source of non-blinding arises with outcome assessment. Where objective measures are taken by a member of the research team, all trial reports properly describe the assessors as blinded, in all trials but one ( 52 ). Some of the outcome measures are participant-reported, which is exclusively the case in six trials ( 35 , 37 , 40 , 43 , 49 , 51 ). Participants were, thus, aware not only of the nature of the intervention, but were also asked to report on the impact of the activity.

A further potential source of bias arises in 15 out of 18 trials as there is no reporting of reliability of data gathered to evaluate the interventions. The JBI appraisal is very clear that the issue is not whether the measures employed had been previously validated, but whether reliability estimates for the data itself are reported. This could readily have been done in two ways: estimates of internal consistency for scales used, or examining correlations between baseline and follow-up assessments, but in only three trials is data reliability reported ( 35 , 44 , 50 , 52 ).

In addition to “internal validity”, the JBI appraisal involves assessing “statistical conclusion validity”. For most trials, follow-up is complete (Q10), or levels of attrition are very low, but for four cases, attrition is quite substantial ( 35 , 36 , 46 , 48 ). This represents a potential source of bias for these trials, as the sample followed up differs from the initially randomised sample. For four trials, however, an intention-to-treat analysis was explicitly employed, and so participants were analysed as randomised (Q11) ( 35 , 41 , 42 , 45 ). For the remainder of the trials where follow up was complete, we judged that participants were analysed as allocated.

The picture is much more varied for Q12, however, on whether the statistical analysis reported was appropriate. Six out of 18 trials were considered to meet exacting demands for statistical analysis ( 35 , 38 , 39 , 42 , 43 , 45 ). Ganzoni et al. ( 39 ), for example, are meticulous regarding their account of the intention-to-treat analysis undertaken with reference to a prospective power calculation and use of two-tailed tests. In addition, they include a clear statement of testing for normality and matching the statistical tests employed to the measurement characteristics of the outcome variables.

For the remaining twelve trials, however, there is no prospective power calculation, and in most cases no reference to MCID scores or effect sizes. Accounts of the statistical analysis adopted may appear satisfactory, but with details lacking (e.g., no information on whether t -tests were one-tailed or two-tailed), and problems with the reporting of results (e.g., a failure to report t -values but only p -values).

In two UK trial reports ( 37 , 41 ), there are also concerns over the details of the statistical strategy adopted, and we discuss the approach adopted in detail to illustrate the threats to validity of the conclusions drawn. Fancourt and Perkins ( 37 ), for example, report no differences in depression across three arms of their trial (singing, play, and usual care) after 10 weeks for their total sample of mothers with scores on the Edinburgh Postnatal Depression Scale of ten or greater. They then focus on a smaller sample of mothers with scores of 13 or greater, and, again, find no differences between the trial arms at 10 weeks. Finally, they focus on changes over the first 6 weeks of the trial and find an apparent faster reduction in depression scores over the first 6 weeks of the trial. However, across the first 6 weeks, there was no difference between change for the singing and play groups. Nevertheless, the conclusion reached focuses on the rate of change in the singing group, and it is claimed that “evidence that singing interventions could speed the rate of recovery in women affected by symptoms of PND… could have clinical relevance”. (p. 120) ( 37 ).

In the case of Philip et al. ( 41 ), the appropriate use of non-parametric techniques where data was not normally distributed, and the intention-to-treat approach are both excellent features of the analysis undertaken, but the use of one-tailed criterion may be criticised as too liberal, as for an exploratory study a two-tailed approach would be recommended ( 56 ). This is especially the case given that the reported p -value for changes in a measure of depression is 0.049—at the very limit for rejecting the null hypothesis, and, thus, far from convincing.

Context of the CultureForHealth report

Societies and healthcare systems all over the world face unprecedented challenges in public health, and pressures on health care services and escalating costs ( 57 ). Evidence-based medicine, despite extraordinary advances, is also limited in what it can offer people with enduring and progressive health conditions. It is undeniable that cross-sector collaboration and inter-disciplinary working is needed to meet these demands. Improvements in public health will only come about by addressing the root causes of ill-health and health inequities, which has been clear since the seminal work of 19 th century social reformers ( 58 ), and which currently are amply reinforced by the work of Marmot on the social determinants of health ( 59 ).

The arts may be one possible sector to integrate into a holistic strategy for improving health and wellbeing in all sectors of society and across the lifespan ( 3 ). The field of arts and health practice and research has indeed made considerable efforts over the last quarter century, and the trials we are considering demonstrate the commitment, passion, and collaborative energy of funding bodies, healthcare professionals, creative artists, and researchers to explore new frontiers in arts and health interventions.

Most of the trials cited in the CultureForHealth report, however, only focus on group singing and dancing, and address specific health issues related to ageing, chronic health conditions, and mental health. As such, the studies may have relevance to addressing just three of the public health challenges identified in the report: the need for greater focus on health promotion, a growing mental health crisis, and an ageing population. In contrast, however, they have little or no relevance to remaining challenges which the report suggests that the arts can help address, such as the need to address the health and wellbeing of young people, addressing health inequalities, and the needs of forcibly displaced people. Moreover, the trials are by no means representative of the international work in arts and health, and many other trials are missing in the report due to its limited search strategy (for example, the report includes three trials concerned with COPD, but misses other key trials published within their time envelope) ( 60 – 62 ). Nevertheless, it is clear that this, albeit selective, corpus demonstrates how global the interest in “creative health” is, with studies as far afield from east to west as China and Brazil, and also in Europe from north to south in the UK and Greece, although no considerations are given in the report on any potential challenges related to drawing conclusions across heterogeneous cultural contexts.

Although scoping reviews do not necessarily involve critical appraisal of the studies included ( 19 , 20 ), the CultureForHealth report's limited research strategy results in even higher risk of bias even at a basic methodological level. Specifically, the report does not offer critical considerations regarding methodological study type and quality, risks of bias, or descriptions of interventions employed. Moreover, the report does not offer critical considerations on the clinical relevance of outcomes and findings to assess the validity of the evidence claims stated, for example regarding the claim that singing improves respiratory function which, however, has not been demonstrated ( 62 – 64 ).

Moreover, no consideration is given to the dangers of drawing conclusions based on underpowered trials ( 65 ). Instead, the authors take findings at face value, and, given the lack of any basic scrutiny, the reporting only meets the very first step in Bloom's taxonomy ( 66 ). Moreover, as demonstrated in the present paper, the included primary RCTs do not meet current standards for good practice regarding developing, investigating, reviewing, and evaluating the benefits of healthcare interventions, nor for rigorous synthesis [e.g., the GRADE framework ( 67 , 68 )].

Notably, in all 18 trial reports, the authors themselves give due attention to the limitations of their studies and the need for further research. This is, however, not clearly transmitted in the report. Moreover, despite previous criticism regarding the methodology and conclusions of the WHO report ( 22 – 24 ), the CultureForHealth report does not address these concerns and presents no clear aim to enhance the methodological quality of research in the field. Immediate confidence in the criticality of reported findings is further compromised e.g., by the identification of a source described as a “systematic review” on singing and health ( 1 , 69 ), which, however, is no more than a spreadsheet of selected studies, even depicting incorrect information, e.g., regarding singing and respiratory function ( 62 , 69 ).

Taken together, the CultureForHealth report ( 1 ), similarly to the WHO report ( 13 ), does not express any hesitations or cautions regarding conclusions and recommendations stated, nor does it sufficiently consider the following aspects:

• Quality and certainty of the evidence ( 29 , 70 );

• Standard frameworks for synthesising the body of evidence regarding complex and health-care interventions, e.g., c.f., the GRADE framework ( 30 , 31 , 71 );

• Patient safety ( 32 , 33 );

• Standards for development/definition of a core outcome set (COS) in health care interventions ( 72 , 73 );

• Standards for evaluating the implementation of healthcare interventions, including acceptability, fidelity, feasibility, scalability, and sustainability ( 74 ).

Thus, based on findings presented in the present paper and the previous concerns raised, we stress the limitations of scoping reviews and grey literature reports which further perpetuate a lack of scientific rigour and trustworthiness within the field. What is needed are systematic reviews which have undergone thorough external peer-review and which properly assess factors relevant to practice and policy development ( 22 , 75 ). We welcome the new Lancet Global Series initiative ( 14 – 16 ) and encourage further high-quality, rigorous research, alongside a fruitful and ambitious academic discussion to form a qualified basis for informing policy and practice. However, we have also found a need to express concerns to the initial opinion piece coming from the Jameel Arts & Health Lab ( 15 , 76 ).

Strengths and limitations of this study

The present paper builds upon previous critiques of reports and research within arts and health, but is the first study to present in-depth scrutiny of the primary studies on which evidence-claims, conclusions, and recommendations are made in the CultureForHealth report. We have approached the exercise of critique with a proper sense of humility and propriety based on an acknowledged framework, and our paper exemplifies the steps and thoroughness needed for assessment and evaluation of primary studies as a basis for drawing conclusions ahead of formulating any evidence-based recommendations for policy or practice. We did not assess or evaluate other study types included in the report (e.g., quasi-experimental and qualitative studies) and further critical scrutiny may be warranted ( 23 ). Given the focus in this paper on the treatment of RCTs, our critique provides a constructive outline and perspectives for future research and provides useful information for readers of the CultureForHealth report.

The CultureForHealth report substantially fails to meet current standards for good practice regarding evaluation of healthcare interventions. The report is not a suitable foundation for policy or practice recommendations nor for current scaled-up implementation of arts for health initiatives. Future trials should adhere to established high-quality standards for the development and evaluation of healthcare interventions, and robust, critical systematic reviews and meta-analyses are needed as a basis for evaluation of the field before considering policy formulation and practice guidelines.

Author contributions

MK: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualisation, Writing – original draft. KG-H: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Supervision, Validation, Writing – original draft. CD: Conceptualisation, Methodology, Resources, Validation, Writing – review & editing. GM: Conceptualisation, Methodology, Resources, Validation, Writing – review & editing. JS: Data curation, Resources, Validation, Writing – review & editing. JM: Conceptualisation, Data curation, Formal analysis, Methodology, Resources, Validation, Writing – review & editing. SC: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualisation, Writing – original draft.

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. KG-H was supported by Land Salzburg. The open access publication costs for article were covered by Paris Lodron University Salzburg, Salzburg, Austria. The funders had no role in the conceptualization, design, literature searches, analysis, interpretations, preparation of the manuscript or decision to publish.

Acknowledgments

The authors would like to thank: Simon Eldaoud, student (Music and Health Research Institute (MHRI), University of Ottawa, Canada), for assistance in the appraisal of selected RCTs; Helena Daffern, Professor, PhD (School of Physics, Engineering and Technology at the University of York, United Kingdom), for feedback on an earlier draft of this paper; Arne C. Bathke, Professor, PhD, Dean (Faculty of Digital and Analytical Sciences, Paris Lodron University Salzburg, Austria), for advice on statistical issues and feedback on an earlier draft of this paper; Timothy Barker, PhD (School of Public Health, Faculty of Health and Medical Sciences, The University of Adelaide, Evidence-based Healthcare Research, JBI Adelaide GRADE Centre, Australia), for guidance on the use of the JBI assessment tool; students (Interuniversity Organisation Science and Art, Department of Musicology and Dance Studies, Paris Lodron University Salzburg, Mozarteum University Salzburg, Salzburg, Austria), for co-assessment of the RCTs on dancing: Antonella Dilber, Hanna Hruba, Lu Lorenz, Khatia Maisarudze, Marie Pichler, Tamara RanXl, Enya Marie Rieder, Emilia Schatzl, Lisa Stelzer, Johanna Wunsch, Berthold Beyerlein, Barbara Bischof, Mark Hebell, Onjeon Lee, Miranda Lipovica, Lily Marie Ludwig, Maryam Rostamivand, Dustin Waskow, Eila Büche, Elena Grolmusz, Kaori Shimada, Rojas Trcka, Rebecca Naß, Ronja Rühmkorff, Elena Schwalbe.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher's note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpubh.2024.1414070/full#supplementary-material

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Keywords: culture, arts and health, scoping reviews, evidence, health policy

Citation: Kaasgaard M, Grebosz-Haring K, Davies C, Musgrave G, Shriraam J, McCrary JM and Clift S (2024) Is it premature to formulate recommendations for policy and practice, based on culture and health research? A robust critique of the CultureForHealth (2022) report. Front. Public Health 12:1414070. doi: 10.3389/fpubh.2024.1414070

Received: 08 April 2024; Accepted: 18 June 2024; Published: 11 July 2024.

Reviewed by:

Copyright © 2024 Kaasgaard, Grebosz-Haring, Davies, Musgrave, Shriraam, McCrary and Clift. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Katarzyna Grebosz-Haring, katarzyna.grebosz-haring@plus.ac.at ; Mette Kaasgaard, mkaasgaard@health.sdu.dk

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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  1. One-Tailed and Two-Tailed Hypothesis Tests Explained

    One-tailed hypothesis tests are also known as directional and one-sided tests because you can test for effects in only one direction. When you perform a one-tailed test, the entire significance level percentage goes into the extreme end of one tail of the distribution. In the examples below, I use an alpha of 5%.

  2. Two-Tailed Hypothesis Tests: 3 Example Problems

    HA (Alternative Hypothesis): μ ≠ 10 inches. This is an example of a two-tailed hypothesis test because the alternative hypothesis contains the not equal "≠" sign. The botanist believes that the new fertilizer will influence plant growth, but doesn't specify whether it will cause average growth to increase or decrease.

  3. An Introduction to Statistics: Understanding Hypothesis Testing and

    The second article in this series on biostatistics covers the concepts of sample, population, research hypotheses and statistical errors. How to cite this article. Ranganathan P, Pramesh CS. ... This is known as a two-tailed hypothesis and it allows us to test for superiority on either side (using a two-sided test). This is because, when we ...

  4. Two Tailed Test: Definition, Examples

    A two tailed test tells you that you're finding the area in the middle of a distribution. In other words, your rejection region (the place where you would reject the null hypothesis) is in both tails. For example, let's say you were running a z test with an alpha level of 5% (0.05). In a one tailed test, the entire 5% would be in a single tail.

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    The one-tailed hypothesis is rejected only if the sample proportion is much greater than \(0.5\). The alternative hypothesis in the two-tailed test is \(\pi \neq 0.5\). In the one-tailed test it is \(\pi > 0.5\). You should always decide whether you are going to use a one-tailed or a two-tailed probability before looking at the data.

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    There are 5 main steps in hypothesis testing: State your research hypothesis as a null hypothesis and alternate hypothesis (H o) and (H a or H 1 ). Collect data in a way designed to test the hypothesis. Perform an appropriate statistical test. Decide whether to reject or fail to reject your null hypothesis. Present the findings in your results ...

  8. One- and two-tailed tests

    In coin flipping, the null hypothesis is a sequence of Bernoulli trials with probability 0.5, yielding a random variable X which is 1 for heads and 0 for tails, and a common test statistic is the sample mean (of the number of heads) ¯. If testing for whether the coin is biased towards heads, a one-tailed test would be used - only large numbers of heads would be significant.

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    At this point, you might use a statistical test, like unpaired or 2-sample t-test, to see if there's a significant difference between the two groups' means. Typically, an unpaired t-test starts with two hypotheses. The first hypothesis is called the null hypothesis, and it basically says there's no difference in the means of the two groups.

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    The decision rule for a specific test depends on 3 factors: the research or alternative hypothesis, the test statistic and the level of significance. Each is discussed below. The decision rule depends on whether an upper-tailed, lower-tailed, or two-tailed test is proposed.

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    To perform a two-tailed test at a significance level of 0.05, you need to divide alpha by 2, giving a significance level of 0.025 for each distribution tail (0.05/2 = 0.025). This is done because the two-tailed test is looking for significance in either tail of the distribution. If the calculated test statistic falls in the rejection region of ...

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    A research hypothesis, in its plural form "hypotheses," is a specific, testable prediction about the anticipated results of a study, established at its outset. ... A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of ...

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    4 One-tailed vs two-tailed test. To gain a deeper understanding of how to conduct a hypothesis test, this section will delve into the concepts of one-tailed and two-tailed tests. These tests are vital tools in statistical hypothesis testing, and the decision of which test to employ depends on the research question and hypothesis under examination.

  15. One-tailed and two-tailed tests (video)

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    First let's start with the meaning of a two-tailed test. If you are using a significance level of 0.05, a two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha to testing statistical significance in the other direction. This means that .025 is in each tail of the distribution ...

  17. One- Versus Two-Tailed Hypothesis Tests in Contemporary Educational

    The choice of a one- rather than a two-tailed hypothesis testing strategy can influence research outcomes, but information about the type of test conducted is rarely reported in articles appearing in educational and psychological journals.

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    represents an inequality. With a one-tailed test, the alternative successful, and thereby publishable, educational research. hypothesis is directional, whereas with a two-tailed test it is nondirectional. For example, a researcher may administer a Current Practice school readiness inventory to preschool girls and boys.

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    Building on our pilot studies and established research, we hypothesize that tail striatal astrocytes actively contribute to neuronal plasticity, supporting changes in auditory perception during associative learning. To test this hypothesis, we propose a series of experiments utilizing established methods from the Xiong

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    The one-tailed hypothesis is rejected only if the sample proportion is much greater than \(0.5\). The alternative hypothesis in the two-tailed test is \(\pi \neq 0.5\). In the one-tailed test it is \(\pi > 0.5\). You should always decide whether you are going to use a one-tailed or a two-tailed probability before looking at the data.

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  27. Frontiers

    To ensure accurate appraisals, a two-stage strategy was employed: Stage 1: Between July 2023 and November 2023, each trial report was appraised independently by two members of the research team for each domain (singing: MK, SC; dance: KG-H, SC; music listening and games: JS, SE). The assessors then met online and discussed their ratings and, where differences of opinion had arisen, an agreed ...