how to write a conclusion for hypothesis testing

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How to Write Hypothesis Test Conclusions (With Examples)

A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

Null Hypothesis (H 0 ): The sample data occurs purely from chance.
Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

Whether we reject or fail to reject the null hypothesis.
The significance level.
A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.

He performs a hypothesis test at a 10% significance level using the following hypotheses:

H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

Published by Zach

How to State the Conclusion about a Hypothesis Test

After you have completed the statistical analysis and decided to reject or fail to reject the Null hypothesis, you need to state your conclusion about the claim. To get the correct wording, you need to recall which hypothesis was the claim.

If the claim was the null, then your conclusion is about whether there was sufficient evidence to reject the claim. Remember, we can never prove the null to be true, but failing to reject it is the next best thing. So, it is not correct to say, “Accept the Null.”

If the claim is the alternative hypothesis, your conclusion can be whether there was sufficient evidence to support (prove) the alternative is true.

Use the following table to help you make a good conclusion.

how to write a conclusion for hypothesis testing

The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself.

For example, if the claim was the alternative that the mean score on a test was greater than 85, and your decision was to Reject then Null , then you could conclude: “ At the 5% significance level, there is sufficient evidence to support the claim that the mean score on the test was greater than 85. ”

The reason you should include the significance level is that the decision, and thus the conclusion, could be different if the significance level was not 5%.

If you are curious why we say “Fail to Reject the Null” instead of “Accept the Null,” this short video might be of interest: Here

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It is concluded that the null hypothesis Ho is not rejected proportion p is greater than 0.5, at the 0.05 significance

People living in rural Idaho community live longer than 77 years

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How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

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).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

An independent variable is something the researcher changes or controls.
A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

The relevant variables
The specific group being studied
The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

Sampling methods
Simple random sampling
Stratified sampling
Cluster sampling
Likert scales
Reproducibility

Statistics

Null hypothesis
Statistical power
Probability distribution
Effect size
Poisson distribution

Research bias

Optimism bias
Cognitive bias
Implicit bias
Hawthorne effect
Anchoring bias
Explicit bias

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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.

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.

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5: Hypothesis Testing, Part 1

Identify and write null and alternative hypotheses
Describe randomization procedures
Determine p-values using randomization methods in StatKey and Minitab
Interpret p-values
Make conclusions on the basis of a p-value

In Lesson 4 we used data from samples to construct confidence intervals for population parameters. When constructing confidence intervals the population parameters were unknown and we were estimating them. In this lesson we will continue to study statistical inference, but here we will be focusing on testing specific hypotheses. Now, we have a hypothesized population parameter to test. This changes how we construct our sampling distribution. Instead of having a distribution centered on the observed sample statistic, we will construct a distribution centered on the hypothesized population parameter.

This lesson corresponds to Sections 4.1, 4.2, and 4.3 in the Lock 5 textbook.

Hypothesis tests use data from a sample to make an inference about the value of a population parameter. In this lesson we will be conducting hypothesis tests with the following parameters:

We can also conduct hypothesis tests with paired means. If data are paired, and the response variable is quantitative, then the outcome of interest is the mean difference. In a population this is $\mu_d$ and in a sample $\overline x_d$. We would first compute the differences for each case, then treat those differences as if they are the variable of interest and conduct a single sample mean test.

5.1 - Introduction to Hypothesis Testing

Previously we used confidence intervals to estimate unknown population parameters. We compared confidence intervals to specified parameter values and when the specific value was contained in the interval, we concluded that there was not sufficient evidence of a difference between the population parameter and the specified value. In other words, any values within the confidence intervals were reasonable estimates of the population parameter and any values outside of the confidence intervals were not reasonable estimates. Here, we are going to look at a more formal method for testing whether a given value is a reasonable value of a population parameter. To do this we need to have a hypothesized value of the population parameter.

In this lesson we will compare data from a sample to a hypothesized parameter. In each case, we will compute the probability that a population with the specified parameter would produce a sample statistic as extreme or more extreme to the one we observed in our sample. This probability is known as the p-value and it is used to evaluate statistical significance.

A test is considered to be statistically significant when the p-value is less than or equal to the level of significance, also known as the alpha ($\alpha$) level. For this class, unless otherwise specified, $\alpha=0.05$; this is the most frequently used alpha level in many fields.

Sample statistics vary from the population parameter randomly. When results are statistically significant, we are concluding that the difference observed between our sample statistic and the hypothesized parameter is unlikely due to random sampling variation.

5.2 - Writing Hypotheses

The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ($H_0$) and an alternative hypothesis ($H_a$).

When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.

At this point we can write hypotheses for a single mean ($\mu$), paired means($\mu_d$), a single proportion ($p$), the difference between two independent means ($\mu_1-\mu_2$), the difference between two proportions ($p_1-p_2$), a simple linear regression slope ($\beta$), and a correlation ($\rho$).
The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., $\mu_0$ and $p_0$). For the difference between two groups, regression, and correlation, this value is typically 0.

Hypotheses are always written in terms of population parameters (e.g., $p$ and $\mu$). The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).

5.2.1 - Examples

Example: rent.

Research question : Is the average monthly rent of a one-bedroom apartment in State College, Pennsylvania less than \$900?

In this question we are comparing the mean of all State College one-bedroom apartments (i.e. $\mu$) to the value of \$900. This is a single sample mean test. We want to know if the population mean is less than \$900, so this is a left-tailed test. Our hypotheses are:

$H_0:\mu=\$900$
$H_a: \mu < \$900$

Example: IQ Scores

Research question : Is the average IQ score of all World Campus STAT 200 students higher than the national average of 100?

In this question we are comparing the mean of all World Campus STAT 200 students (i.e. $\mu$) to the given value of 100. This is a single sample mean test. We want to know if the population mean is greater than 100, so this is a right-tailed test. Our hypotheses are:

$H_0:\mu = 100$
$H_a: \mu > 100$

Example: Weight Loss

Research question: Do participants lose weight following a weight-loss intervention?

Data were collected from one group of participants before and after a weight-loss intervention. Data were paired by participant. Assuming that $x_1$ is an individual's weight before the intervention and $x_2$ is their weight at the end of the study, if they lost weight then $x_1-x_2$ would be a positive number (i.e., greater than 0). Thus, this is a right-tailed test. Because we are testing their mean difference, the parameter that we should write in our hypotheses is $\mu_d$ where $\mu_d$ is the mean weight change (before-after) in the population.

Our hypotheses are:

$H_0: \mu_d=0$
$H_a:\mu_d > 0 $

Example: Gender of College of Science Students

Research question : Is the percent of students enrolled in Penn State's College of Science who identify as women different from 50%?

In this question we are comparing the proportion of all Penn State College of Science students (i.e. $p$) to the given value of 0.5. This is a single sample proportion test. We want to know if the population proportion is different from 0.5, so this is a two-tailed test. Our hypotheses are:

$H_0:p=0.5$
$H_a: p ≠ 0.5$

Example: Dog Ownership

Research question : Do the majority of all World Campus STAT 200 students own a dog?

If the majority of all students own a dog, then more than 50% own a dog. In this question we are comparing the population proportion for all World Campus STAT 200 students (i.e. $p$) to the value of 0.5. This is a single sampling proportion test. We want to know if the proportion is greater than 0.5, so this is a right-tailed test. Our hypotheses are:

$H_a: p > 0.5$

Example: Weights of Boys and Girls

Research question : In preschool, are the weights of boys and girls different?

We are comparing the weights of two independent groups: boys and girls. Weight is a quantitative variable so the parameter we are testing is $\mu$. Our research question does not hypothesize which group has the larger weight, so this is a two-tailed test. Our hypotheses are:

$H_0: \mu_b = \mu_g$
$H_a: \mu_b \ne \mu_g$

Note: This is equivalent to $H_0: \mu_b - \mu_g = 0$ and $H_a: \mu_b - \mu_g \ne 0$.

Example: Smoking by Gender

Research question : Is the proportion of men who smoke cigarettes different from the proportion of women who smoke cigarettes in the United States?

In this question we are comparing two independent groups: men and women. The response variable, smoking, is categorical therefore we are comparing proportions. Our research question does not suggest which group smokes more, so we have a two-tailed test. Our hypotheses are:

$H_0: p_1=p_2$
$H_a: p_1 \ne p_2$

Note: This is equivalent to $H_0: p_1 - p_2 =0$ and $H_a: p_1 - p_2 \ne 0$

Example: Predicting SAT-Math using IQ

Research question : Can IQ scores be used to predict SAT-Math scores in the population of all American high school seniors?

SAT-Math and IQ scores are both quantitative variables. Our research question is about prediction, so we are going to use simple linear regression. The parameter we are testing is $\beta$. Our research question does not state whether we expect the slope to be positive or negative, therefore this is a two-tailed test. Our hypotheses are:

$H_0: \beta = 0$
$H_a: \beta \ne 0$

Example: Relation Between Height and Weight

Research question : Is there a positive relationship between height and weight in the population of all American adults age 25 and older?

The relationship between two quantitative variables is measured using correlation (Pearson's r). The parameter we are testing is $\rho$. A positive relationship would be indicated by a positive correlation coefficient, therefore this is a right-tailed test. Our hypotheses are:

$H_0: \rho = 0$

$H_a: \rho > 0$

5.3 - Randomization Procedures

Like bootstrapping procedures, randomization procedures use resampling techniques to construct a sampling distribution that can be used to make inferences about the population. What makes a randomization distribution different is that it is constructed given that the null hypothesis is true. The randomization distribution will be centered on the value in the null hypothesis.

StatKey can be used to construct a randomization distribution for a single mean, single proportion, difference in means, difference in proportions, the slope of a simple linear regression model, or a correlation (Pearson's r ). Minitab can conduct a randomization test for a single mean, single proportion, or difference in means.

The video below walks through an example of using StatKey to construct a randomization distribution. It also looks ahead to the next section and uses that randomization distribution to determine the p-value.

These are the steps that we will be using to conduct hypothesis tests this semester:

Determine what type of test you need to conduct and write the hypotheses.
Construct a randomization distribution under the assumption that the null hypothesis is true.
Use the randomization distribution to find the p-value.
Decide if you should reject or fail to reject the null hypothesis.
State a real-world conclusion in relation to the original research question.

Here, you learned how to complete Step 2. On the next page you will learn how to use this randomization distribution to complete Steps 3 through 5.

5.3.1 - StatKey Randomization Methods (Optional)

The following information goes beyond what you are expected to know for this course. Here, details about all of the randomization procedure options available in StatKey are covered. In STAT 200 you will always be using the default randomization methods. The information here is optional and is meant to provide extra details to individuals who are interested in learning more, beyond what is required of most introductory statistics courses.

Randomization Test for One Mean

In StatKey there is only one method for conducting a randomization test for one mean. The sample is shifted so that the sample mean equals the hypothesized population mean (i.e., the value in the null hypothesis). Samples of the same size as the original sample are drawn with replacement from the shifted distribution and the mean of each randomization sample is recorded on the randomization distribution dotplot.

Randomization Test for One Proportion

In StatKey there is only one method for conducting a randomization test for one proportion. Samples of the same size as the original sample are drawn from a theoretical distribution with a proportion equal to the hypothesized population proportion (i.e., the value in the null hypothesis).The sample proportion in each randomization sample is recorded on the randomization distribution dotplot.

Randomization Test for a Difference in Means

StatKey offers three randomization methods when comparing the means of two independent groups: reallocate groups, shift groups, and combine groups. In this course we will always be using the default method of reallocating groups. For larger sample sizes results will be relatively consistent across the three methods. In practice, the method that is most appropriate may depend on the design of the research study. For example, the reallocation method may be preferred in studies where participants were randomly assigned to different conditions.

Reallocate Groups This is the default method in StatKey. In this course, this is always the method that will be used. Using the reallocate method, all cases in the samples are combined and then randomly assigned to the two groups with the same sample sizes as the original samples. This is done without replacement. The mean of each reallocated sample is recorded. The difference between those reallocated sample's means is recorded on the randomization distribution dotplot.
Shift Groups The two groups are shifted until their observed sample means are equal. This is similar to the method used for one sample mean. After the groups are shifted, cases are randomly selected from the first group, with replacement, until a randomization sample of the same size as the first group's original sample is obtained. This procedure is followed for the second group as well. The difference between the mean of the first group and the mean of the second group is recorded on the randomization distribution plot.
Combine Groups All cases in the samples are combined and then randomly selected with replacement. Again, the sample sizes for each group will be equal to each group's original sample size. The difference between this combine groups method and the default reallocate groups method is that this method resamples with replacement so an original case can appear more than once in a group, in both groups, or not at all.

Randomization Test for a Difference in Proportions

StatKey offers two randomization methods when comparing the proportions of two independent groups: reallocation and resampling. In this course we will be using the default reallocation method.

Reallocation This procedure is the same as the reallocate groups procedure for two group means. All cases are combined and then randomly assigned to between the two groups with the same sample sizes as the original samples. This is done without replacement so the total number of successes between the two groups will always be equal to the total number of successes between the two groups.
Resampling The two groups are combined and the overall observed proportion is computed. Samples of the same size as the original samples are drawn from a theoretical distribution with a proportion equal to the overall observed proportion. The differences between the sample proportions in the two randomization samples are recorded on the randomization distribution dotplot.

Randomization Test for a Slope, Correlation

The randomization methods used for testing the slope and correlation are the same as both procedures involve two quantitative variables. In each case, the pairs of x and y variables are separated and randomly assigned to new pairs. The slope or correlation between those new pairs is computed and recorded on the randomization distribution plot. Like the other reallocation methods, this is done without replacement so each case's x value and y value are only selected once.

Online discussion including textbook author Robin Lock https://groups.google.com/forum/#!topic/lock5stat/AG45cIcy018
Lock Morgan, K., Lock, R. H., Frazer Lock, P., Lock, E. F., Lock, D. F. (2014). StatKey: Online tools for bootstrap intervals and randomization tests. Paper presented at the International Conference on Teaching Statistics (ICOTS9). Flagstaff, AZ. https://iase-web.org/icots/9/proceedings/pdfs/ICOTS9_9B2_LOCKMORGAN.pdf

5.4 - p-values

We can use a randomization distribution to determine how likely our sample statistic is given that the null hypothesis is true. This probability is known as the p-value . The p-value is the proportion of samples on the randomization distribution that are more extreme than our observed sample in the direction of the alternative hypothesis. The p-value is compared to the alpha level (typically 0.05).

Making a Decision

If $p > \alpha$ then we "fail to reject the null hypothesis" and conclude that there is not enough evidence of a difference in the population. This does not mean that the null hypothesis is true, it only means that we do not have sufficient evidence to say that it is likely false. These results are not statistically significant.

If $p \leq \alpha$ then we "reject the null hypothesis" and conclude that there is a difference in the population. These results are statistically significant.

5.5 - Randomization Test Examples in StatKey

The following pages contain examples of conducting randomization tests using StatKey .

5.5.1 - Single Proportion Example: PA Residency

This example uses data collected from World Campus STAT 200 students at the beginning of the Fall 2016 semester. You can download this Minitab file here: fall2016stdata.mpx

Research question : Are less than half of all World Campus STAT 200 students Pennsylvania residents?

This research question is asking if there is evidence that the population proportion is less than 0.50 which can be translated to the following hypotheses:

$H_0: p=0.50$

$H_a: p \lt 0.50$

Step 1 : We are comparing the proportion in one group to 0.50. This is a one sample proportion test.

Step 2 : We used StatKey to construct a randomization distribution.

Step 3 : $p<0.001$

Step 4 : $p \leq 0.05$, reject the null hypothesis

Step 5 : There is evidence that the proportion of all World Campus STAT 200 students who are Pennsylvania residents is less than 0.50.

5.5.2 - Paired Means Example: Age

Research question: On average, are husbands older than their wives?

Step 1: The data are paired by couple. This is a paired means test.

$H_0: \mu_d=0$

$H_a: \mu_d > 0$

Step 2: We constructed a randomization distribution in StatKey using the built in dataset.

Step 3: $p < 0.001$

Step 4: Reject the null hypothesis

Step 5: There is evidence that in the population, on average, husbands are older than their wives.

5.5.3 - Difference in Means Example: Exercise by Biological Sex

Do males and females differ in terms of how many hours per week they exercise? This example uses a dataset that is built in to StatKey .

Step 1 : Hours exercised per week is a quantitative variable and we are comparing two independent groups. We should conduct a hypothesis test for the differences in means.

$H_0: \mu_m = \mu_f$

$H_a: \mu_m \ne \mu_f$

Step 2 : We constructed the randomization distribution given that there is not a difference between the means of males and females.

Step 3 : $p = 0.114+0.114=0.228$

Step 4 : $p>0.05$, we should fail to reject the null hypothesis

Step 5 : There is not enough evidence that the mean number of hours per week exercised by males and females is different in the population. Our results are not statistically significant.

5.5.4 - Correlation Example: Quiz & Exam Scores

Using the sample data in:

We want to know if there is evidence of a positive relationship between quiz scores and final exam scores in the population of all World Campus STAT 200 students. If there is a positive relationship, then the population correlation would be greater than zero. This can be translated to the following hypotheses:

Step 1 : We are examining the relationship between two quantitative variables. We should compute and test Pearson's r which is a correlation coefficient.

Step 2 : We constructed a randomization distribution given that the correlation in the population is 0.

Step 3 : $p<0.001$

Step 4 : $p\leq 0.05$, we should reject the null hypothesis

Step 5 : There is evidence of a positive relationship between quiz scores and final exam scores in the population of all World Campus STAT 200 students.

5.6 - Lesson 5 Summary

Identify and write null and alternative hypotheses.
Describe randomization procedures.
Determine p-values using randomization methods in StatKey and Minitab.
Interpret p-values.
Make conclusions on the basis of a p-value.

Let's review the randomization test procedures that you learned in this lesson:

Determine what type of test you need to conduct and write the hypotheses
Construct a randomization distribution under the assumption that the null hypothesis is true
Use the randomization distribution to find the p-value
Decide if you should reject or fail to reject the null hypothesis (see below)
State a real-world conclusion in relation to the original research question

If $p>\alpha$ then we fail to reject the null hypothesis and there is not enough evidence to support the alternative hypothesis. These results are said to be not statistically significant. If $p \le \alpha$ then we reject the null hypothesis and conclude that there is enough evidence to support the alternative hypothesis. These results are statistically significant. Unless otherwise stated, $\alpha$ of 0.05 should be used.

We will be using these same hypothesis testing steps in all of the remaining lessons.

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How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, frequently asked questions about writing hypotheses.

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Prevent plagiarism, run a free check.

Step 1: ask a question.

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2: Do some preliminary research

At this stage, you might construct a conceptual framework to identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

The relevant variables
The specific group being studied
The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

Step 6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

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).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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Hypothesis Testing – A Complete Guide with Examples

Published by Alvin Nicolas at August 14th, 2021 , Revised On October 26, 2023

In statistics, hypothesis testing is a critical tool. It allows us to make informed decisions about populations based on sample data. Whether you are a researcher trying to prove a scientific point, a marketer analysing A/B test results, or a manufacturer ensuring quality control, hypothesis testing plays a pivotal role. This guide aims to introduce you to the concept and walk you through real-world examples.

What is a Hypothesis and a Hypothesis Testing?

A hypothesis is considered a belief or assumption that has to be accepted, rejected, proved or disproved. In contrast, a research hypothesis is a research question for a researcher that has to be proven correct or incorrect through investigation.

What is Hypothesis Testing?

Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an independent variable to a dependent variable.

Example: The academic performance of student A is better than student B

Characteristics of the Hypothesis to be Tested

A hypothesis should be:

Clear and precise
Capable of being tested
Able to relate to a variable
Stated in simple terms
Consistent with known facts
Limited in scope and specific
Tested in a limited timeframe
Explain the facts in detail

What is a Null Hypothesis and Alternative Hypothesis?

A null hypothesis is a hypothesis when there is no significant relationship between the dependent and the participants’ independent variables .

In simple words, it’s a hypothesis that has been put forth but hasn’t been proved as yet. A researcher aims to disprove the theory. The abbreviation “Ho” is used to denote a null hypothesis.

If you want to compare two methods and assume that both methods are equally good, this assumption is considered the null hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is similar to the previous model of the car, on average. You can write it as: Ho: there is no difference between the mileage of both vehicles. If your findings don’t support your hypothesis and you get opposite results, this outcome will be considered an alternative hypothesis.

If you assume that one method is better than another method, then it’s considered an alternative hypothesis. The alternative hypothesis is the theory that a researcher seeks to prove and is typically denoted by H1 or HA.

If you support a null hypothesis, it means you’re not supporting the alternative hypothesis. Similarly, if you reject a null hypothesis, it means you are recommending the alternative hypothesis.

Example: In an automobile trial, you feel that the new vehicle’s mileage is better than the previous model of the vehicle. You can write it as; Ha: the two vehicles have different mileage. On average/ the fuel consumption of the new vehicle model is better than the previous model.

If a null hypothesis is rejected during the hypothesis test, even if it’s true, then it is considered as a type-I error. On the other hand, if you don’t dismiss a hypothesis, even if it’s false because you could not identify its falseness, it’s considered a type-II error.

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How to Conduct Hypothesis Testing?

Here is a step-by-step guide on how to conduct hypothesis testing.

Step 1: State the Null and Alternative Hypothesis

Once you develop a research hypothesis, it’s important to state it is as a Null hypothesis (Ho) and an Alternative hypothesis (Ha) to test it statistically.

A null hypothesis is a preferred choice as it provides the opportunity to test the theory. In contrast, you can accept the alternative hypothesis when the null hypothesis has been rejected.

Example: You want to identify a relationship between obesity of men and women and the modern living style. You develop a hypothesis that women, on average, gain weight quickly compared to men. Then you write it as: Ho: Women, on average, don’t gain weight quickly compared to men. Ha: Women, on average, gain weight quickly compared to men.

Step 2: Data Collection

Hypothesis testing follows the statistical method, and statistics are all about data. It’s challenging to gather complete information about a specific population you want to study. You need to gather the data obtained through a large number of samples from a specific population.

Example: Suppose you want to test the difference in the rate of obesity between men and women. You should include an equal number of men and women in your sample. Then investigate various aspects such as their lifestyle, eating patterns and profession, and any other variables that may influence average weight. You should also determine your study’s scope, whether it applies to a specific group of population or worldwide population. You can use available information from various places, countries, and regions.

Step 3: Select Appropriate Statistical Test

There are many types of statistical tests , but we discuss the most two common types below, such as One-sided and two-sided tests.

Note: Your choice of the type of test depends on the purpose of your study

One-sided Test

In the one-sided test, the values of rejecting a null hypothesis are located in one tail of the probability distribution. The set of values is less or higher than the critical value of the test. It is also called a one-tailed test of significance.

Example: If you want to test that all mangoes in a basket are ripe. You can write it as: Ho: All mangoes in the basket, on average, are ripe. If you find all ripe mangoes in the basket, the null hypothesis you developed will be true.

Two-sided Test

In the two-sided test, the values of rejecting a null hypothesis are located on both tails of the probability distribution. The set of values is less or higher than the first critical value of the test and higher than the second critical value test. It is also called a two-tailed test of significance.

Example: Nothing can be explicitly said whether all mangoes are ripe in the basket. If you reject the null hypothesis (Ho: All mangoes in the basket, on average, are ripe), then it means all mangoes in the basket are not likely to be ripe. A few mangoes could be raw as well.

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Step 4: Select the Level of Significance

When you reject a null hypothesis, even if it’s true during a statistical hypothesis, it is considered the significance level . It is the probability of a type one error. The significance should be as minimum as possible to avoid the type-I error, which is considered severe and should be avoided.

If the significance level is minimum, then it prevents the researchers from false claims.

The significance level is denoted by P, and it has given the value of 0.05 (P=0.05)

If the P-Value is less than 0.05, then the difference will be significant. If the P-value is higher than 0.05, then the difference is non-significant.

Example: Suppose you apply a one-sided test to test whether women gain weight quickly compared to men. You get to know about the average weight between men and women and the factors promoting weight gain.

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

After conducting a statistical test, you should identify whether your null hypothesis is rejected or accepted based on the test results. It would help if you observed the P-value for this.

Example: If you find the P-value of your test is less than 0.5/5%, then you need to reject your null hypothesis (Ho: Women, on average, don’t gain weight quickly compared to men). On the other hand, if a null hypothesis is rejected, then it means the alternative hypothesis might be true (Ha: Women, on average, gain weight quickly compared to men. If you find your test’s P-value is above 0.5/5%, then it means your null hypothesis is true.

Step 6: Present the Outcomes of your Study

The final step is to present the outcomes of your study . You need to ensure whether you have met the objectives of your research or not.

In the discussion section and conclusion , you can present your findings by using supporting evidence and conclude whether your null hypothesis was rejected or supported.

In the result section, you can summarise your study’s outcomes, including the average difference and P-value of the two groups.

If we talk about the findings, our study your results will be as follows:

Example: In the study of identifying whether women gain weight quickly compared to men, we found the P-value is less than 0.5. Hence, we can reject the null hypothesis (Ho: Women, on average, don’t gain weight quickly than men) and conclude that women may likely gain weight quickly than men.

Did you know in your academic paper you should not mention whether you have accepted or rejected the null hypothesis?

Always remember that you either conclude to reject Ho in favor of Haor do not reject Ho . It would help if you never rejected Ha or even accept Ha .

Suppose your null hypothesis is rejected in the hypothesis testing. If you conclude reject Ho in favor of Haor do not reject Ho, then it doesn’t mean that the null hypothesis is true. It only means that there is a lack of evidence against Ho in favour of Ha. If your null hypothesis is not true, then the alternative hypothesis is likely to be true.

Example: We found that the P-value is less than 0.5. Hence, we can conclude reject Ho in favour of Ha (Ho: Women, on average, don’t gain weight quickly than men) reject Ho in favour of Ha. However, rejected in favour of Ha means (Ha: women may likely to gain weight quickly than men)

Frequently Asked Questions

What are the 3 types of hypothesis test.

The 3 types of hypothesis tests are:

One-Sample Test : Compare sample data to a known population value.
Two-Sample Test : Compare means between two sample groups.
ANOVA : Analyze variance among multiple groups to determine significant differences.

What is a hypothesis?

A hypothesis is a proposed explanation or prediction about a phenomenon, often based on observations. It serves as a starting point for research or experimentation, providing a testable statement that can either be supported or refuted through data and analysis. In essence, it’s an educated guess that drives scientific inquiry.

What are null hypothesis?

A null hypothesis (often denoted as H0) suggests that there is no effect or difference in a study or experiment. It represents a default position or status quo. Statistical tests evaluate data to determine if there’s enough evidence to reject this null hypothesis.

What is the probability value?

The probability value, or p-value, is a measure used in statistics to determine the significance of an observed effect. It indicates the probability of obtaining the observed results, or more extreme, if the null hypothesis were true. A small p-value (typically <0.05) suggests evidence against the null hypothesis, warranting its rejection.

What is p value?

The p-value is a fundamental concept in statistical hypothesis testing. It represents the probability of observing a test statistic as extreme, or more so, than the one calculated from sample data, assuming the null hypothesis is true. A low p-value suggests evidence against the null, possibly justifying its rejection.

What is a t test?

A t-test is a statistical test used to compare the means of two groups. It determines if observed differences between the groups are statistically significant or if they likely occurred by chance. Commonly applied in research, there are different t-tests, including independent, paired, and one-sample, tailored to various data scenarios.

When to reject null hypothesis?

Reject the null hypothesis when the test statistic falls into a predefined rejection region or when the p-value is less than the chosen significance level (commonly 0.05). This suggests that the observed data is unlikely under the null hypothesis, indicating evidence for the alternative hypothesis. Always consider the study’s context.

8.1: Steps in Hypothesis Testing

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CHAPTER OBJECTIVES

By the end of this chapter, the student should be able to:

Differentiate between Type I and Type II Errors
Describe hypothesis testing in general and in practice
Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.
Conduct and interpret hypothesis tests for a single population proportion

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter. Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealer advertises that its new small truck gets 35 miles per gallon, on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that women managers in their company earn an average of $60,000 per year.

A statistician will make a decision about these claims. This process is called "hypothesis testing." A hypothesis test involves collecting data from a sample and evaluating the data. Then, the statistician makes a decision as to whether or not there is sufficient evidence, based upon analysis of the data, to reject the null hypothesis. In this chapter, you will conduct hypothesis tests on single means and single proportions. You will also learn about the errors associated with these tests.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will:

Set up two contradictory hypotheses.
Collect sample data (in homework problems, the data or summary statistics will be given to you).
Determine the correct distribution to perform the hypothesis test.
Analyze sample data by performing the calculations that ultimately will allow you to reject or decline to reject the null hypothesis.
Make a decision and write a meaningful conclusion.

To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. See Appendix E .

The desired confidence level.
Information that is known about the distribution (for example, known standard deviation).
The sample and its size.

How to Write Hypothesis Test Conclusions (With Examples)

A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

Null Hypothesis (H 0 ): The sample data occurs purely from chance.
Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

Whether we reject or fail to reject the null hypothesis.
The significance level.
A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

He performs a hypothesis test at a 10% significance level using the following hypotheses:

H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

10 Examples of Using Probability in Real Life

Mongodb: how to find document by id, related posts, how to normalize data between -1 and 1, vba: how to check if string contains another..., how to interpret f-values in a two-way anova, how to create a vector of ones in..., how to find the mode of a histogram..., how to find quartiles in even and odd..., how to determine if a probability distribution is..., what is a symmetric histogram (definition & examples), how to calculate sxy in statistics (with example), how to calculate sxx in statistics (with example).

Hypothesis Testing: A Step-by-Step Guide With Easy Examples

Introduction

When we hear the word ‘hypothesis,’ the first thing that comes to our mind is a kind of theory. Assuming and explaining theories is a fundamental part of Business Analytics. In the past few years, the field of Business Analytics has proliferated and made several advancements. As the number of people interested in its statistical applications in business has increased, the concept of hypothesis testing has grabbed everyone’s attention.

Let us find out more about testing of hypothesis and the different steps through which you can write a hypothesis.

What is Hypothesis?

A hypothesis’s general definition says, “Hypothesis is an assumption made based on some evidence.” It is a theory you propose about what will happen in the future based on current circumstances. Proposing a hypothesis is the first and most important step of any research or investigation as it decides the future path of the research/investigation and can lead it to a faithful and acceptable answer.

Key Points of a Hypothesis

The assumptions made while proposing the theory should be precise and based on proper evidence.
The hypothesis should target a specific topic only and should have the scope to conduct various experiments for proving the assumptions.
The sources used for developing a hypothesis must be based on scientific theories, common patterns that affect the thought process of the people, and observations made in past research programs on the same topic.

Types of Hypotheses With Examples

There are multiple types of hypotheses which are described below.

1. Simple Hypothesis

As the name suggests, a simple hypothesis is pretty simple to work on. It just deals with a single independent variable and one dependent variable. While proving a simple hypothesis, you just have to confirm that these two variables are linked.

Example: If you eat more vegetables, you will be safe from heart disease. Here eating vegetables is an independent variable and staying safe from heart disease is a dependent variable.

2. Complex Hypothesis

Unlike a simple hypothesis, a complex hypothesis deals with multiple dependent and independent variables in the assumption simultaneously. The involvement of multiple variables makes the hypothesis more accurate and more difficult to prove simultaneously.

Example: Age, diet, and weight affect the chances of diseases like diabetes or blood pressure. Age, diet, and weight are independent variables, and diabetes and blood pressure are dependent variables.

3. Null Hypothesis

The null hypothesis is the opposite of the simple hypothesis. Where a simple hypothesis tries to establish a link between the dependent and the independent variables, the Null hypothesis tries to prove that there’s no link between the given variables. Simply put, it tries to prove a statement opposite to the proposed hypothesis. It is represented as H0.

Example: Age and daily routine affect the chances of heart disease. In a Null hypothesis, you will try to prove that there is no relation between the given factors, i.e., age, weight, and heart disease.

4. Alternative Hypothesis

An alternative hypothesis tries to disapprove the assumptions or statements proposed in a null hypothesis. Generally, alternative and null hypotheses are used together. An alternative hypothesis is represented as HA.

It is to be noted that H0 ≠ H A. The alternate hypothesis further branches into two categories:

Directional Hypothesis: The result obtained through this type of alternative hypothesis is either negative or positive. It is represented by adding ‘>’ or ‘<‘ along with the HA symbol.
Non-Directional Hypothesis: This type of hypothesis only clarifies the dependency of the dependent variables on the independent variable. It does not state anything about the result being positive or negative.

Example:

Age and daily routine affect the chances of heart disease. In an Alternative Hypothesis, you will try to prove that age and daily routine affect heart disease chances.

If you prove the result is positive or negative, i.e., age and daily routine do or do not affect the chances of heart disease, it is a directional hypothesis
If you only prove that the chances of heart disease depend on variables like age and daily routine, it is a non-directional hypothesis.

5. Logical Hypothesis

Logical hypotheses cannot be proved with the help of scientific evidence. The assumptions made in a logical hypothesis are based on some logical explanation that backs up our assumptions. Logical hypotheses are mostly used in philosophy, and as the assumptions made are often too complex or simply unrealistic, they are untestable, and we have to rely on logical explanations.

Example:

Dinosaurs are related to the reptile family as both have scales. As the dinosaurs are extinct, we cannot test the given hypothesis and rely on our logical explanation on, not the experimental data.

6. Empirical Hypothesis

It is the complete opposite of the Logical Hypothesis. The assumptions made in an Empirical Hypothesis are based on empirical data and proved through scientific testing and analysis.

It is divided into two parts, namely theoretical and empirical. Both methods of research rely on testing that can be verified through experimental data. So, unlike logical hypotheses, an empirical hypothesis can be and will be tested.

Vegetables grow faster in cold climates as compared to warm and humid climates. The assumption stated here can be thoroughly tested through scientific methods.

7. Statistical Hypothesis

Statistical Hypothesis makes use of large statistical datasets to obtain results that consider larger populations. This type of hypothesis is used when we have to take into consideration all the possible cases present in the assumptions made in the hypothesis. It makes use of datasets or samples so that conclusions can be drawn from the broader dataset. For this, you may conduct tests for sufficient samples and obtain results with high accuracy that would remain stable across all the datasets.

Men in the U.S.A. are taller than men in India. It is simply impossible to measure the height of all the men present in India and the U.S.A., but by conducting the test on sufficient samples, you can obtain results with high accuracy that would remain constant over different samples.

What Makes a Good Hypothesis?

Before developing a good hypothesis, you must consider a few points.

Do the assumptions made in the hypothesis consist of dependent or independent variables?
Can you conduct safety tests for your assumptions in the hypothesis?
Are there any other alternative assumptions present that you can take into consideration?

Characteristics of a Good Hypothesis –

1. Candid Language

Make use of simple language in your hypothesis instead of being vague. Try to focus on the given topic through your assumptions; it should be simple yet justifiable. The use of candid language makes the hypothesis more understandable and reachable to the common people.

2. Cause and Effect

Understand the assumptions made in the hypothesis. For example, the cause of the assumption, the effect of the assumption being accepted or rejected, etc. Try to back up your assumptions with the help of proper scientific data and explanations.

3. The Independent and Dependent Variables

Before starting to write a hypothesis, figure out the number of dependent and independent variables in the hypothesis. This will help you make proper assumptions to establish a link between these variables or to prove that these variables are not interlinked. It will also help you to prepare a mind map for your hypothesis.

4. Accurate Results

One of the most important characteristics of a good hypothesis is the accuracy of the results. Hypotheses are generally used to predict the future based on current scenarios. This can help to figure out the problems that may arise in the future and find solutions accordingly.

5. Adherence to Ethics

Sticking to ethics while working on any research project is very important. You get an idea about the research structure through the generally followed ethics beforehand. It helps to guide the research project or hypothesis in a fruitful direction.

6. Testable Predictions

The conditions used in the hypothesis research project should be easily testable. This helps to make the results of the hypothesis more accurate and reliable. Before starting the research on the assumptions in the hypothesis, you should be aware of all the different ways that can be used to make the hypothesis applicable to modern testing methodologies.

How to Write a Hypothesis?

Well, there are many ways to write a hypothesis; here are the six most efficient and important steps that will help you craft a strong hypothesis:

Step 1: Ask a Question

The first and most important step of writing a hypothesis is deciding upon the questions or assumptions you will implement in your research. A hypothesis can’t be based on random questions or general thoughts. The questions you decide must be approachable and testable as it forms the foundation of your project.

Step 2: Carry out Preliminary Research

Once you have decided on the questions and assumptions to be included in your hypothesis, you should start your preliminary research on the same. For that, you should start reading older research papers on the topic, go through the web, collect the data, prepare the dataset for the experiments, etc.

Step 3: Define Your Variables

After conducting the preliminary research, you need to define the number of variables present in your assumption and classify them into dependent and independent variables. It will help you to conduct further research and establish a link between them or prove that there is no link between them.

Step-4: Collect Data to Support Your Hypothesis

After classifying the variables and conducting the basic preliminary research, you need to start collecting evidence and data that will help you support your hypothesis. This data will help you test your assumptions and infer statistical results about your interesting dataset.

Step-5: Perform Statistical Tests

The data you have collected from the above step can be used to perform different statistical tests. The type of tests you perform depends on the data you collect. All the different tests are based on in-group variance and between-group variance. Depending on the variance, your statistical test will reflect a high or low p-value.

After performing the tests, you should prepare a draft for writing down your hypothesis.

Step-6: Present It in an If-Then Form

Now that everything has been done, it is time to write down your hypothesis. Considering your draft, you should write down the hypothesis accordingly and ensure that it satisfies all the conditions like simple and to-the-point language, accurate results, relevant evidence and data sources, etc. The final hypothesis should be well-framed and address the topic clearly.

Conclusion

Research and hypothesis testing are an important part of the Business Analytics field. To write a good hypothesis or research, you need to conduct a good amount of research. Since you know about the different types of hypotheses and how to write a good hypothesis, writing a good and strong hypothesis by yourself is now much easier! If you want to pursue a career in the field of Business Analytics, you can check out the Integrated Program In Business Analytics by UNext Jigsaw. We hope now you understand “ what is hypothesis testing ?” and hypothesis testing steps in detail.

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Statement of the Conclusion

When writing your results, you’re going to write the decision regarding the null, but you also want to state the results in layman’s terms. Tie the statistical results back to the original claim and interpret what those statistics mean, without all the quantitative jargon.

1) Claim : Females run faster than males. Results of the test : t o > t c Decision : Reject Null Hypothesis. Conclusion : There is sufficient evidence to suggest that females run faster than males.

2) Claim : There is a difference in the highest level of education obtained based on socioeconomic status. Results of the test : p > α Decision : Fail to Reject Null Hypothesis. Conclusion : There is not enough evidence to suggest that highest level of education differs based on socioeconomic status.

3) Claim : The number of calories consumed and the number of hours spent exercising each week are significant predictors of weight. Results of the test : p < α Decision : Reject Null Hypothesis. Conclusion : The results of the hypothesis test suggest that a person’s weight can be predicted given caloric intake and the number of hours spent exercising each week.

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How to Write Hypothesis Test Conclusions (With Examples)

A hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

Null Hypothesis (H 0 ): The sample data occurs purely from chance.
Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

Whether we reject or fail to reject the null hypothesis.
The significance level.
A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

He performs a hypothesis test at a 10% significance level using the following hypotheses:

H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

10 Examples of Using Probability in Real Life

Mongodb: how to find document by id, you may also like, how to normalize data between -1 and 1, vba: how to check if string contains another string, how to interpret f-values in a two-way anova, how to create a vector of ones in r (with examples), how to find the mode of a histogram (with example), how to find quartiles in even and odd length datasets.

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AP®︎/College Statistics

Course: ap®︎/college statistics > unit 10.

Idea behind hypothesis testing
Examples of null and alternative hypotheses
Writing null and alternative hypotheses
P-values and significance tests
Comparing P-values to different significance levels
Estimating a P-value from a simulation
Estimating P-values from simulations

Using P-values to make conclusions

(Choice A) Fail to reject H 0 ‍ A Fail to reject H 0 ‍
(Choice B) Reject H 0 ‍ and accept H a ‍ B Reject H 0 ‍ and accept H a ‍
(Choice C) Accept H 0 ‍ C Accept H 0 ‍
(Choice A) The evidence suggests that these subjects can do better than guessing when identifying the bottled water. A The evidence suggests that these subjects can do better than guessing when identifying the bottled water.
(Choice B) We don't have enough evidence to say that these subjects can do better than guessing when identifying the bottled water. B We don't have enough evidence to say that these subjects can do better than guessing when identifying the bottled water.
(Choice C) The evidence suggests that these subjects were simply guessing when identifying the bottled water. C The evidence suggests that these subjects were simply guessing when identifying the bottled water.
(Choice A) She would have rejected H a ‍ . A She would have rejected H a ‍ .
(Choice B) She would have accepted H 0 ‍ . B She would have accepted H 0 ‍ .
(Choice C) She would have rejected H 0 ‍ and accepted H a ‍ . C She would have rejected H 0 ‍ and accepted H a ‍ .
(Choice D) She would have reached the same conclusion using either α = 0.05 ‍ or α = 0.10 ‍ . D She would have reached the same conclusion using either α = 0.05 ‍ or α = 0.10 ‍ .
(Choice A) The evidence suggests that these bags are being filled with a mean amount that is different than 7.4 kg ‍ . A The evidence suggests that these bags are being filled with a mean amount that is different than 7.4 kg ‍ .
(Choice B) We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4 kg ‍ . B We don't have enough evidence to say that these bags are being filled with a mean amount that is different than 7.4 kg ‍ .
(Choice C) The evidence suggests that these bags are being filled with a mean amount of 7.4 kg ‍ . C The evidence suggests that these bags are being filled with a mean amount of 7.4 kg ‍ .
(Choice A) They would have rejected H a ‍ . A They would have rejected H a ‍ .
(Choice B) They would have accepted H 0 ‍ . B They would have accepted H 0 ‍ .
(Choice C) They would have failed to reject H 0 ‍ . C They would have failed to reject H 0 ‍ .
(Choice D) They would have reached the same conclusion using either α = 0.05 ‍ or α = 0.01 ‍ . D They would have reached the same conclusion using either α = 0.05 ‍ or α = 0.01 ‍ .

Ethics and the significance level α ‍

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How to Write Hypothesis Test Conclusions (With Examples)

Table of Contents

A hypothesis test conclusion is the outcome of the test, which is based on the results of the test statistic and the value of the critical value. To write a hypothesis test conclusion, it is important to compare the test statistic to the critical value and decide if it is significantly different. If it is, then the null hypothesis is rejected and the alternative hypothesis is accepted. If the test statistic is not significantly different, then the null hypothesis is accepted. Examples of hypothesis test conclusions include “the difference in the means is significant” or “the difference in the means is not significant.”

A is used to test whether or not some hypothesis about a is true.

To perform a hypothesis test in the real world, researchers obtain a from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

Null Hypothesis (H 0 ): The sample data occurs purely from chance.
Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

Whether we reject or fail to reject the null hypothesis.
The significance level.
A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

We reject the null hypothesis at the 5% significance level. There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

He performs a hypothesis test at a 10% significance level using the following hypotheses:

H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level. There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

The following tutorials provide additional information about hypothesis testing:

Related terms:

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How to Write a Great Hypothesis

Hypothesis Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk, "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis, operational definitions, types of hypotheses, hypotheses examples.

Collecting Data

Frequently Asked Questions

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study.

One hypothesis example would be a study designed to look at the relationship between sleep deprivation and test performance might have a hypothesis that states: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

Forming a question
Performing background research
Creating a hypothesis
Designing an experiment
Collecting data
Analyzing the results
Drawing conclusions
Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. It is only at this point that researchers begin to develop a testable hypothesis. Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore a number of factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk wisdom that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

Is your hypothesis based on your research on a topic?
Can your hypothesis be tested?
Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the journal articles you read . Many authors will suggest questions that still need to be explored.

To form a hypothesis, you should take these steps:

Collect as many observations about a topic or problem as you can.
Evaluate these observations and look for possible causes of the problem.
Create a list of possible explanations that you might want to explore.
After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method , falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that if something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in a number of different ways. One of the basic principles of any type of scientific research is that the results must be replicable. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. How would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

In order to measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming other people. In this situation, the researcher might utilize a simulated task to measure aggressiveness.

Hypothesis Checklist

Does your hypothesis focus on something that you can actually test?
Does your hypothesis include both an independent and dependent variable?
Can you manipulate the variables?
Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

Simple hypothesis : This type of hypothesis suggests that there is a relationship between one independent variable and one dependent variable.
Complex hypothesis : This type of hypothesis suggests a relationship between three or more variables, such as two independent variables and a dependent variable.
Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative sample of the population and then generalizes the findings to the larger group.
Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

"Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
Complex hypothesis: "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."
"Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."

Examples of a complex hypothesis include:

"People with high-sugar diets and sedentary activity levels are more likely to develop depression."
"Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

"Children who receive a new reading intervention will have scores different than students who do not receive the intervention."
"There will be no difference in scores on a memory recall task between children and adults."

Examples of an alternative hypothesis:

"Children who receive a new reading intervention will perform better than students who did not receive the intervention."
"Adults will perform better on a memory task than children."

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as case studies , naturalistic observations , and surveys are often used when it would be impossible or difficult to conduct an experiment . These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a correlational study can then be used to look at how the variables are related. This type of research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually cause another to change.

A Word From Verywell

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Some examples of how to write a hypothesis include:

"Staying up late will lead to worse test performance the next day."
"People who consume one apple each day will visit the doctor fewer times each year."
"Breaking study sessions up into three 20-minute sessions will lead to better test results than a single 60-minute study session."

The four parts of a hypothesis are:

The research question
The independent variable (IV)
The dependent variable (DV)
The proposed relationship between the IV and DV

Castillo M. The scientific method: a need for something better? . AJNR Am J Neuroradiol. 2013;34(9):1669-71. doi:10.3174/ajnr.A3401

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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The Craft of Writing a Strong Hypothesis

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

A research hypothesis has to be simple yet clear to look justifiable enough.
It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1. Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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How To Conduct Hypothesis Testing In R For Effective Data Analysis

Learn the essentials of hypothesis testing in R, a crucial skill for developers. This article guides you through setting up your environment, formulating hypotheses, executing tests, and interpreting results with practical examples

💡 KEY INSIGHTS

Hypothesis testing involves using a random population sample to test the null and alternative hypotheses , where the null hypothesis typically represents equality between population parameters.
The null hypothesis (H0) assumes no event occurrence and is critical unless rejected, while the alternate hypothesis (H1) is its logical opposite and is considered upon the rejection of H0.
The p-value is a crucial metric in hypothesis testing, indicating the likelihood of an observed difference occurring by chance; a lower p-value suggests a higher probability of the alternate hypothesis being true.
Hypothesis testing is significant in research methodology as it provides evidence-based conclusions , supports decision-making , adds rigor and validity , and contributes to the advancement of knowledge in various fields.

Hypothesis testing in R is a fundamental skill for programmers and developers looking to analyze and interpret data effectively. This article guides you through the essential steps and techniques, using R's robust statistical tools. Whether you're new to R or seeking to refine your data analysis skills, these insights will enhance your ability to make data-driven decisions.

Setting Up Your R Environment

Formulating and testing your hypothesis, interpreting test results, frequently asked questions.

Before diving into hypothesis testing, ensure you have R and RStudio installed. R is the programming language used for statistical computing, while RStudio provides an integrated development environment (IDE) to work with R. Download R from CRAN and RStudio from RStudio's website.

Configuring Your Workspace

Installing necessary packages, loading data into r, exploratory data analysis, basic data manipulation.

After installation, open RStudio and set up your workspace. This involves organizing your scripts, data files, and outputs. Use setwd() to define your working directory:

R's functionality is extended through packages. For hypothesis testing, packages like ggplot2 for data visualization and stats for statistical functions are essential. Install packages using install.packages() :

After installation, load them into your session using library() :

Data can be loaded into R using various functions depending on the file format. For a CSV file, use read.csv() :

Before hypothesis testing, it's crucial to understand your data. Use summary functions and visualization to explore:

Data often requires cleaning and manipulation. Functions like subset() and transform() are useful:

These commands help in refining your dataset, making it ready for hypothesis testing.

The first step in hypothesis testing is to Formulate a Clear Hypothesis . This typically involves stating a null hypothesis (H0) that indicates no effect or no difference, and an alternative hypothesis (H1) that suggests the presence of an effect or a difference.

Null And Alternative Hypothesis

Choosing the right test, t-test example, interpreting the results, analyzing the output, visualizing the data.

For example, if you're testing whether a new programming tool improves efficiency:

H0: The tool does not improve efficiency.
H1: The tool improves efficiency.

Selecting an appropriate statistical test is crucial. The choice depends on your data type and the nature of your hypothesis. Common tests include t-tests, chi-square tests, and ANOVA.

If you're comparing means between two groups, a t-test is appropriate. In R, use t.test() :

The output of t.test() includes the P-Value , which helps determine the significance of your results. A p-value lower than your significance level (commonly 0.05) indicates that you can reject the null hypothesis.

After running t.test() , analyze the output:

P-Value : Indicates the probability of observing your data if the null hypothesis is true.
Confidence Interval : Provides a range in which the true mean difference likely lies.

Visualizing your data can provide additional insights. For instance, use ggplot2 to create a plot that compares the groups:

Understanding P-Values

Interpreting confidence intervals, effect size, calculating and interpreting effect size, creating a plot for results.

The P-Value is central in interpreting hypothesis test results. It represents the probability of observing your data, or something more extreme, if the null hypothesis is true. A small p-value (typically ≤ 0.05) suggests that the observed data is unlikely under the null hypothesis, leading to its rejection.

Evaluating Significance

When you run a test, R provides a p-value:

Confidence Intervals

Confidence Intervals offer a range of values within which the true parameter value lies with a certain level of confidence (usually 95%). Narrow intervals indicate more precise estimates.

From your test output, extract and examine the confidence interval:

While p-values indicate whether an effect exists, the Effect Size measures its magnitude. It's crucial for understanding the practical significance of your results.

For a t-test, you might calculate Cohen's d:

For instance, create a plot to visualize the difference:

What is Effect Size and Why is it Important?

Effect size is a quantitative measure of the magnitude of the experimental effect. Unlike p-values, which tell you if an effect exists, effect size tells you how large that effect is. It's important for understanding the practical significance of your results.

How Do I Interpret a Confidence Interval?

A confidence interval gives a range of values within which the true value is likely to lie. For example, a 95% confidence interval means that if the same study were repeated many times, 95% of the intervals would contain the true value.

What Does 'Rejecting the Null Hypothesis' Mean in Practical Terms?

Rejecting the null hypothesis suggests that there is enough statistical evidence to support the alternative hypothesis. In practical terms, it means that the observed effect or difference is unlikely to be due to chance.

Can I Perform Hypothesis Testing on Non-Numeric Data?

Yes, you can perform hypothesis testing on non-numeric (categorical) data. Tests like the Chi-Square test are designed for categorical data and can test hypotheses about proportions or frequencies.

Let’s test your knowledge!

What is the function used in R to perform a t-test?

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Hypothesis Testing in Statistical Theory
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Lecture 10 Ch 2 hypothesis testing 17 3 2024

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How to Write Hypothesis Test Conclusions (With Examples)
When writing the conclusion of a hypothesis test, we typically include: Whether we reject or fail to reject the null hypothesis. The significance level. A short explanation in the context of the hypothesis test. For example, we would write: We reject the null hypothesis at the 5% significance level.
Hypothesis Testing
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 ...
How to State the Conclusion about a Hypothesis Test
Use the following table to help you make a good conclusion. The best way to state the conclusion is to include the significance level of the test and a bit about the claim itself. " At the 5% significance level, there is sufficient evidence to support the claim that the mean score on the test was greater than 85.
5.2
5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). Null Hypothesis. The statement that there is not a difference in the population (s), denoted as H 0.
How to Write a Strong Hypothesis
5. Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
5: Hypothesis Testing, Part 1
The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ($H_0$) and an alternative hypothesis ($H_a$). ... Decide if you should reject or fail to reject the null hypothesis. State a real-world conclusion in relation to the original ...
A Complete Guide to Hypothesis Testing
Photo from StepUp Analytics. Hypothesis testing is a method of statistical inference that considers the null hypothesis H₀ vs. the alternative hypothesis Ha, where we are typically looking to assess evidence against H₀. Such a test is used to compare data sets against one another, or compare a data set against some external standard. The former being a two sample test (independent or ...
How to Write a Strong Hypothesis
Step 5: Phrase your hypothesis in three ways. To identify the variables, you can write a simple prediction in if … then form. The first part of the sentence states the independent variable and the second part states the dependent variable. If a first-year student starts attending more lectures, then their exam scores will improve.
Hypothesis Testing
Hypothesis testing is a scientific method used for making a decision and drawing conclusions by using a statistical approach. It is used to suggest new ideas by testing theories to know whether or not the sample data supports research. A research hypothesis is a predictive statement that has to be tested using scientific methods that join an ...
8.1: Steps in Hypothesis Testing
Figure 8.1.1 8.1. 1: You can use a hypothesis test to decide if a dog breeder's claim that every Dalmatian has 35 spots is statistically sound. (Credit: Robert Neff) A statistician will make a decision about these claims. This process is called "hypothesis testing." A hypothesis test involves collecting data from a sample and evaluating the data.
Significance tests (hypothesis testing)
Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values to make conclusions about hypotheses.
How to Write Hypothesis Test Conclusions (With Examples)
When writing the conclusion of a hypothesis test, we typically include: Whether we reject or fail to reject the null hypothesis. The significance level. A short explanation in the context of the hypothesis test. For example, we would write: We reject the null hypothesis at the 5% significance level.
Hypothesis Testing: A Step-by-Step Guide With Easy Examples
Conclusion . Research and hypothesis testing are an important part of the Business Analytics field. To write a good hypothesis or research, you need to conduct a good amount of research. Since you know about the different types of hypotheses and how to write a good hypothesis, writing a good and strong hypothesis by yourself is now much easier!
Statement of Conclusion
Examples: 1) Claim: Females run faster than males. Results of the test: to > tc. Decision: Reject Null Hypothesis. Conclusion: There is sufficient evidence to suggest that females run faster than males. 2) Claim: There is a difference in the highest level of education obtained based on socioeconomic status. Results of the test: p > α.
Hypothesis Testing
Step 2: State the Alternate Hypothesis. The claim is that the students have above average IQ scores, so: H 1: μ > 100. The fact that we are looking for scores "greater than" a certain point means that this is a one-tailed test. Step 3: Draw a picture to help you visualize the problem. Step 4: State the alpha level.
T-test and Hypothesis Testing (Explained Simply)
Aug 5, 2022. 6. Photo by Andrew George on Unsplash. Student's t-tests are commonly used in inferential statistics for testing a hypothesis on the basis of a difference between sample means. However, people often misinterpret the results of t-tests, which leads to false research findings and a lack of reproducibility of studies.
How to Write Hypothesis Test Conclusions (With Examples)
This tutorial explains how to write hypothesis test conclusions, including examples.
Using P-values to make conclusions (article)
Onward! We use p -values to make conclusions in significance testing. More specifically, we compare the p -value to a significance level α to make conclusions about our hypotheses. If the p -value is lower than the significance level we chose, then we reject the null hypothesis H 0 in favor of the alternative hypothesis H a .
Hypothesis Testing with Python: Step by step hands-on tutorial with
Image by the author. 4. Decision and Conclusion. After performing the hypothesis testing, we obtain a related p-value that shows the significance of the test.. If the p-value is smaller than the alpha (the significance level), in other words, there is enough evidence to prove H₀ is not valid; you can reject H₀.Otherwise, you fail to reject H₀.
How to Write Hypothesis Test Conclusions (With Examples)
When writing the conclusion of a hypothesis test, we typically include: Whether we reject or fail to reject the null hypothesis. The significance level. A short explanation in the context of the hypothesis test. For example, we would write: We reject the null hypothesis at the 5% significance level.
How to Write a Great Hypothesis
What is a hypothesis and how can you write a great one for your research? A hypothesis is a tentative statement about the relationship between two or more variables that can be tested empirically. Find out how to formulate a clear, specific, and testable hypothesis with examples and tips from Verywell Mind, a trusted source of psychology and mental health information.
The Craft of Writing a Strong Hypothesis
Simple hypothesis. A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, "Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking. 4.
How To Conduct Hypothesis Testing In R For Effective ...
Formulating And Testing Your Hypothesis. The first step in hypothesis testing is to Formulate a Clear Hypothesis. This typically involves stating a null hypothesis (H0) that indicates no effect or no difference, and an alternative hypothesis (H1) that suggests the presence of an effect or a difference. Null And Alternative Hypothesis.

How to Write Hypothesis Test Conclusions (With Examples)

Example 1: Reject the Null Hypothesis Conclusion

Example 2: Fail to Reject the Null Hypothesis Conclusion

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How to State the Conclusion about a Hypothesis Test

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How to Write a Strong Hypothesis | Steps & Examples

Example: Hypothesis

Table of contents

Variables in hypotheses

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Step 1. Ask a question

Step 2. Do some preliminary research

Step 3. Formulate your hypothesis

4. Refine your hypothesis

5. Phrase your hypothesis in three ways

6. Write a null hypothesis

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5: Hypothesis Testing, Part 1

5.1 - Introduction to Hypothesis Testing

5.2 - Writing Hypotheses

5.2.1 - Examples

Example: IQ Scores

Example: Weight Loss

Example: Gender of College of Science Students

Example: Dog Ownership

Example: Weights of Boys and Girls

Example: Smoking by Gender

Example: Predicting SAT-Math using IQ

Example: Relation Between Height and Weight

5.3 - Randomization Procedures

5.3.1 - StatKey Randomization Methods (Optional)

5.4 - p-values

Making a Decision

5.5 - Randomization Test Examples in StatKey

5.5.1 - Single Proportion Example: PA Residency

5.5.2 - Paired Means Example: Age

5.5.3 - Difference in Means Example: Exercise by Biological Sex

5.5.4 - Correlation Example: Quiz & Exam Scores

5.6 - Lesson 5 Summary

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How to Write a Strong Hypothesis | Guide & Examples

Table of contents

Variables in hypotheses

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Step 2: Do some preliminary research

Step 3: Formulate your hypothesis

Step 4: Refine your hypothesis

Step 5: Phrase your hypothesis in three ways

Step 6. Write a null hypothesis

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Shona McCombes

Hypothesis Testing – A Complete Guide with Examples

What is a Hypothesis and a Hypothesis Testing?

What is Hypothesis Testing?

Characteristics of the Hypothesis to be Tested

What is a Null Hypothesis and Alternative Hypothesis?

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How to Conduct Hypothesis Testing?

Step 1: State the Null and Alternative Hypothesis

Step 2: Data Collection

Step 3: Select Appropriate Statistical Test

One-sided Test

Two-sided Test

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Step 4: Select the Level of Significance

Step 5: Find out Whether the Null Hypothesis is Rejected or Supported

Step 6: Present the Outcomes of your Study

Frequently Asked Questions

What is a hypothesis?

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