meaning of hypothesis test in economics

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1.3 The Economists’ Tool Kit

Learning objectives.

• Explain how economists test hypotheses, develop economic theories, and use models in their analyses.
• Explain how the all-other-things unchanged (ceteris paribus) problem and the fallacy of false cause affect the testing of economic hypotheses and how economists try to overcome these problems.
• Distinguish between normative and positive statements.

Economics differs from other social sciences because of its emphasis on opportunity cost, the assumption of maximization in terms of one’s own self-interest, and the analysis of choices at the margin. But certainly much of the basic methodology of economics and many of its difficulties are common to every social science—indeed, to every science. This section explores the application of the scientific method to economics.

Researchers often examine relationships between variables. A variable is something whose value can change. By contrast, a constant is something whose value does not change. The speed at which a car is traveling is an example of a variable. The number of minutes in an hour is an example of a constant.

Research is generally conducted within a framework called the scientific method , a systematic set of procedures through which knowledge is created. In the scientific method, hypotheses are suggested and then tested. A hypothesis is an assertion of a relationship between two or more variables that could be proven to be false. A statement is not a hypothesis if no conceivable test could show it to be false. The statement “Plants like sunshine” is not a hypothesis; there is no way to test whether plants like sunshine or not, so it is impossible to prove the statement false. The statement “Increased solar radiation increases the rate of plant growth” is a hypothesis; experiments could be done to show the relationship between solar radiation and plant growth. If solar radiation were shown to be unrelated to plant growth or to retard plant growth, then the hypothesis would be demonstrated to be false.

If a test reveals that a particular hypothesis is false, then the hypothesis is rejected or modified. In the case of the hypothesis about solar radiation and plant growth, we would probably find that more sunlight increases plant growth over some range but that too much can actually retard plant growth. Such results would lead us to modify our hypothesis about the relationship between solar radiation and plant growth.

If the tests of a hypothesis yield results consistent with it, then further tests are conducted. A hypothesis that has not been rejected after widespread testing and that wins general acceptance is commonly called a theory . A theory that has been subjected to even more testing and that has won virtually universal acceptance becomes a law . We will examine two economic laws in the next two chapters.

Even a hypothesis that has achieved the status of a law cannot be proven true. There is always a possibility that someone may find a case that invalidates the hypothesis. That possibility means that nothing in economics, or in any other social science, or in any science, can ever be proven true. We can have great confidence in a particular proposition, but it is always a mistake to assert that it is “proven.”

Models in Economics

All scientific thought involves simplifications of reality. The real world is far too complex for the human mind—or the most powerful computer—to consider. Scientists use models instead. A model is a set of simplifying assumptions about some aspect of the real world. Models are always based on assumed conditions that are simpler than those of the real world, assumptions that are necessarily false. A model of the real world cannot be the real world.

We will encounter our first economic model in Chapter 35 “Appendix A: Graphs in Economics” . For that model, we will assume that an economy can produce only two goods. Then we will explore the model of demand and supply. One of the assumptions we will make there is that all the goods produced by firms in a particular market are identical. Of course, real economies and real markets are not that simple. Reality is never as simple as a model; one point of a model is to simplify the world to improve our understanding of it.

Economists often use graphs to represent economic models. The appendix to this chapter provides a quick, refresher course, if you think you need one, on understanding, building, and using graphs.

Models in economics also help us to generate hypotheses about the real world. In the next section, we will examine some of the problems we encounter in testing those hypotheses.

Testing Hypotheses in Economics

Here is a hypothesis suggested by the model of demand and supply: an increase in the price of gasoline will reduce the quantity of gasoline consumers demand. How might we test such a hypothesis?

Economists try to test hypotheses such as this one by observing actual behavior and using empirical (that is, real-world) data. The average retail price of gasoline in the United States rose from an average of $2.12 per gallon on May 22, 2005 to $2.88 per gallon on May 22, 2006. The number of gallons of gasoline consumed by U.S. motorists rose 0.3% during that period.

The small increase in the quantity of gasoline consumed by motorists as its price rose is inconsistent with the hypothesis that an increased price will lead to an reduction in the quantity demanded. Does that mean that we should dismiss the original hypothesis? On the contrary, we must be cautious in assessing this evidence. Several problems exist in interpreting any set of economic data. One problem is that several things may be changing at once; another is that the initial event may be unrelated to the event that follows. The next two sections examine these problems in detail.

The All-Other-Things-Unchanged Problem

The hypothesis that an increase in the price of gasoline produces a reduction in the quantity demanded by consumers carries with it the assumption that there are no other changes that might also affect consumer demand. A better statement of the hypothesis would be: An increase in the price of gasoline will reduce the quantity consumers demand, ceteris paribus. Ceteris paribus is a Latin phrase that means “all other things unchanged.”

But things changed between May 2005 and May 2006. Economic activity and incomes rose both in the United States and in many other countries, particularly China, and people with higher incomes are likely to buy more gasoline. Employment rose as well, and people with jobs use more gasoline as they drive to work. Population in the United States grew during the period. In short, many things happened during the period, all of which tended to increase the quantity of gasoline people purchased.

Our observation of the gasoline market between May 2005 and May 2006 did not offer a conclusive test of the hypothesis that an increase in the price of gasoline would lead to a reduction in the quantity demanded by consumers. Other things changed and affected gasoline consumption. Such problems are likely to affect any analysis of economic events. We cannot ask the world to stand still while we conduct experiments in economic phenomena. Economists employ a variety of statistical methods to allow them to isolate the impact of single events such as price changes, but they can never be certain that they have accurately isolated the impact of a single event in a world in which virtually everything is changing all the time.

In laboratory sciences such as chemistry and biology, it is relatively easy to conduct experiments in which only selected things change and all other factors are held constant. The economists’ laboratory is the real world; thus, economists do not generally have the luxury of conducting controlled experiments.

The Fallacy of False Cause

Hypotheses in economics typically specify a relationship in which a change in one variable causes another to change. We call the variable that responds to the change the dependent variable ; the variable that induces a change is called the independent variable . Sometimes the fact that two variables move together can suggest the false conclusion that one of the variables has acted as an independent variable that has caused the change we observe in the dependent variable.

Consider the following hypothesis: People wearing shorts cause warm weather. Certainly, we observe that more people wear shorts when the weather is warm. Presumably, though, it is the warm weather that causes people to wear shorts rather than the wearing of shorts that causes warm weather; it would be incorrect to infer from this that people cause warm weather by wearing shorts.

Reaching the incorrect conclusion that one event causes another because the two events tend to occur together is called the fallacy of false cause . The accompanying essay on baldness and heart disease suggests an example of this fallacy.

Because of the danger of the fallacy of false cause, economists use special statistical tests that are designed to determine whether changes in one thing actually do cause changes observed in another. Given the inability to perform controlled experiments, however, these tests do not always offer convincing evidence that persuades all economists that one thing does, in fact, cause changes in another.

In the case of gasoline prices and consumption between May 2005 and May 2006, there is good theoretical reason to believe the price increase should lead to a reduction in the quantity consumers demand. And economists have tested the hypothesis about price and the quantity demanded quite extensively. They have developed elaborate statistical tests aimed at ruling out problems of the fallacy of false cause. While we cannot prove that an increase in price will, ceteris paribus, lead to a reduction in the quantity consumers demand, we can have considerable confidence in the proposition.

Normative and Positive Statements

Two kinds of assertions in economics can be subjected to testing. We have already examined one, the hypothesis. Another testable assertion is a statement of fact, such as “It is raining outside” or “Microsoft is the largest producer of operating systems for personal computers in the world.” Like hypotheses, such assertions can be demonstrated to be false. Unlike hypotheses, they can also be shown to be correct. A statement of fact or a hypothesis is a positive statement .

Although people often disagree about positive statements, such disagreements can ultimately be resolved through investigation. There is another category of assertions, however, for which investigation can never resolve differences. A normative statement is one that makes a value judgment. Such a judgment is the opinion of the speaker; no one can “prove” that the statement is or is not correct. Here are some examples of normative statements in economics: “We ought to do more to help the poor.” “People in the United States should save more.” “Corporate profits are too high.” The statements are based on the values of the person who makes them. They cannot be proven false.

Because people have different values, normative statements often provoke disagreement. An economist whose values lead him or her to conclude that we should provide more help for the poor will disagree with one whose values lead to a conclusion that we should not. Because no test exists for these values, these two economists will continue to disagree, unless one persuades the other to adopt a different set of values. Many of the disagreements among economists are based on such differences in values and therefore are unlikely to be resolved.

Key Takeaways

• Economists try to employ the scientific method in their research.
• Scientists cannot prove a hypothesis to be true; they can only fail to prove it false.
• Economists, like other social scientists and scientists, use models to assist them in their analyses.
• Two problems inherent in tests of hypotheses in economics are the all-other-things-unchanged problem and the fallacy of false cause.
• Positive statements are factual and can be tested. Normative statements are value judgments that cannot be tested. Many of the disagreements among economists stem from differences in values.

Look again at the data in Table 1.1 “LSAT Scores and Undergraduate Majors” . Now consider the hypothesis: “Majoring in economics will result in a higher LSAT score.” Are the data given consistent with this hypothesis? Do the data prove that this hypothesis is correct? What fallacy might be involved in accepting the hypothesis?

Case in Point: Does Baldness Cause Heart Disease?

Mark Hunter – bald – CC BY-NC-ND 2.0.

A website called embarrassingproblems.com received the following email:

What did Dr. Margaret answer? Most importantly, she did not recommend that the questioner take drugs to treat his baldness, because doctors do not think that the baldness causes the heart disease. A more likely explanation for the association between baldness and heart disease is that both conditions are affected by an underlying factor. While noting that more research needs to be done, one hypothesis that Dr. Margaret offers is that higher testosterone levels might be triggering both the hair loss and the heart disease. The good news for people with early balding (which is really where the association with increased risk of heart disease has been observed) is that they have a signal that might lead them to be checked early on for heart disease.

Source: http://www.embarrassingproblems.com/problems/problempage230701.htm .

Answer to Try It! Problem

The data are consistent with the hypothesis, but it is never possible to prove that a hypothesis is correct. Accepting the hypothesis could involve the fallacy of false cause; students who major in economics may already have the analytical skills needed to do well on the exam.

Principles of Economics Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

• A-Z Publications

Annual Review of Economics

Volume 2, 2010, review article, hypothesis testing in econometrics.

• Joseph P. Romano 1 , Azeem M. Shaikh 2 , and Michael Wolf 3
• View Affiliations Hide Affiliations Affiliations: 1 Departments of Economics and Statistics, Stanford University, Stanford, California 94305; email: [email protected] 2 Department of Economics, University of Chicago, Chicago, Illinois 60637 3 Institute for Empirical Research in Economics, University of Zürich, CH-8006 Zürich, Switzerland
• Vol. 2:75-104 (Volume publication date September 2010) https://doi.org/10.1146/annurev.economics.102308.124342
• First published as a Review in Advance on February 09, 2010
• © Annual Reviews

This article reviews important concepts and methods that are useful for hypothesis testing. First, we discuss the Neyman-Pearson framework. Various approaches to optimality are presented, including finite-sample and large-sample optimality. Then, we summarize some of the most important methods, as well as resampling methodology, which is useful to set critical values. Finally, we consider the problem of multiple testing, which has witnessed a burgeoning literature in recent years. Along the way, we incorporate some examples that are current in the econometrics literature. While many problems with well-known successful solutions are included, we also address open problems that are not easily handled with current technology, stemming from such issues as lack of optimality or poor asymptotic approximations.

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Publication Date: 04 Sep 2010

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Quickonomics

Hypothesis Testing

Definition of hypothesis testing.

Hypothesis testing is a statistical method used to make inferences or decisions about a population based on sample data. It involves formulating a null hypothesis (H 0 ) that represents a statement of no effect or no difference, and an alternative hypothesis (H a or H 1 ), which contradicts the null hypothesis. The goal is to determine whether there is enough evidence from the sample data to reject the null hypothesis in favor of the alternative hypothesis.

Consider a company that claims its new diet pill helps individuals lose more than 10 pounds in a month. To test this claim, a researcher could set up a hypothesis test where the null hypothesis (H 0 ) states that the mean weight loss is less than or equal to 10 pounds, and the alternative hypothesis (H a ) states that the mean weight loss is greater than 10 pounds. The researcher then selects a sample of individuals to take the diet pill, monitors their weight loss over a month, and uses statistical analysis to determine whether the observed data provides sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Why Hypothesis Testing Matters

Hypothesis testing is a cornerstone of scientific research and data analysis, enabling researchers and data scientists to make informed decisions based on empirical evidence. It is widely used across various fields such as medicine, psychology, marketing, and economics, helping to validate theories, compare groups, and assess the effectiveness of treatments or interventions. By providing a systematic way to evaluate claims and make conclusions based on sample data, hypothesis testing reduces the risks of making false assertions about a population.

Frequently Asked Questions (FAQ)

What is the significance level in hypothesis testing.

The significance level, denoted as α, is the probability of rejecting the null hypothesis when it is actually true, known as a Type I error. Common significance levels include 0.05, 0.01, and 0.10. Choosing a lower significance level reduces the likelihood of making a Type I error but makes it more difficult to detect a true effect.

What is the p-value in hypothesis testing?

The p-value is the probability of obtaining test results at least as extreme as the observed data, assuming the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, leading researchers to reject it in favor of the alternative hypothesis.

What are Type I and Type II errors?

A Type I error occurs when the null hypothesis is incorrectly rejected when it is true. A Type II error happens when the null hypothesis is not rejected when it is false (i.e., missing a true effect). The balance between minimizing Type I and Type II errors is critical in the design of hypothesis tests.

How does sample size affect hypothesis testing?

The sample size impacts the power of a hypothesis test, which is the probability of correctly rejecting the null hypothesis when it is false (i.e., detecting a true effect). Larger sample sizes generally increase the test’s power, reducing the likelihood of a Type II error, and providing more reliable results.

Hypothesis testing is essential in data-driven decision-making, providing a framework to objectively assess the validity of claims and theories based on statistical evidence. By understanding and correctly applying hypothesis testing methods, researchers and analysts can draw meaningful conclusions and make informed decisions that are crucial for advancing knowledge and guiding actions in various domains.

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

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

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

There are 5 main steps in hypothesis testing:

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

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

Table of contents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Methodology

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

Research bias

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

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

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

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

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

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Hypothesis Testing

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• First Online: 01 January 2024
• pp 3328–3329
• Cite this reference work entry

• Panagiotis Liargovas 2  

Test statistic

Hypothesis testing is a way of systematically quantifying how certain is the result of a statistical experiment. It is a common practice in science that involves conducting tests and experiments to see if a proposed explanation for an observed phenomenon works in practice (Good 2000 ).

Description

It is one of the most important tools of applied statistics to real life problems and is used to determine the probability that a given hypothesis is true or not (Johnson and Bhattacharya 1992 ). In any field of science, from physics and chemistry to economics and sociology, practitioners often pursue questions using this method. A hypothesis is a tentative explanation for some kind of observed phenomenon and is an important part of the scientific method. A hypothesis is a proposition or statement about the world confronted with facts and thus can be refuted or confirmed by those facts. This kind of test is a way for obtaining results based on a hypothesis...

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Good, P. (2000). Permutation tests: A practical guide to resampling methods for testing hypotheses (2nd ed.). New York: Springer.

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Johnson, R. A., & Bhattacharya, G. K. (1992). Statistics: Principles and methods (2nd ed.). New York: John Wiley and Sons.

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Kennedy, P. (1998). A guide to econometrics (4th ed.). Cambridge, MA: MIT Press.

Lehman, E. L. (1997). Testing statistical hypotheses (2nd reprint ed.). New York: Springer.

Schefler, W. C. (1988). Statistics: Concepts and applications . Redwood City: The Benjamin/Cummings Publishing.

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How does one do a hypothesis test for elasticity?

Given the regression output $$\widehat{\ln cons} = \underset{(0.6018)}{0.4054} + \underset{(0.0744)}{1.2739}\, \ln m - \underset{(0.1902)}{0.6666}\, \ln p_1 -\underset{(0.2645)}{1.6146}\, \ln p_2$$ where $\ln cons$ is the log of chocolate consumption, $\ln m$ is the log of income, $\ln p_1$ is the log of the price of chocolate, and $\ln p_2$ is the log of the price of sweets, test whether chocolate is a luxury good.

Since $1.27 > 1$ , it is logical to test whether $\beta_{\ln m}$ could be less than $1$ . When I test elasticity, I base the null hypothesis on what is logical, as in this case if $\beta_{\ln m}$ is significantly greater than $1$ , one shouldn't reject a (illogical) null hypothesis $\mathrm H_0: \beta_{\ln m} \geq 1$ . So,

$\mathrm H_0: \beta_{\ln m} \leq 1$

$\mathrm H_1: \beta_{\ln m} > 1$

$\displaystyle t = \frac{1.2739-1}{0.0744}\approx 3.681$

Therefore, I reject the null hypothesis in favour of the alternative that chocolates are a luxury good.

Do you agree with the way I have set up this hypothesis test? If the estimate were less than 1, I would have stated $\mathrm H_0: \beta_{\ln m} \geq 1$ against the alternative $\mathrm H_1: \beta_{\ln m} < 1$ .

• econometrics
• hypothesis-testing
• $\begingroup$ A t-statistic that high has less than a 0.01% chance of occurring under the null hypothesis, which is very good evidence that it should be rejected. $\endgroup$ –  Nuclear Hoagie Commented Apr 29, 2019 at 17:30
• $\begingroup$ @NuclearWang sorry! I mangled my interpretation. But that wasn't the point of the question, so please accept my edit. $\endgroup$ –  ahorn Commented Apr 29, 2019 at 18:03
• $\begingroup$ what is indicated by values e.g. (0.0744 ) in the regression output and how do you interpret ) ? $\endgroup$ –  Subhash C. Davar Commented Aug 3, 2019 at 12:12
• $\begingroup$ "test whether chocolate is a luxury good." This needs a clear version and goal of your study. $\endgroup$ –  Subhash C. Davar Commented Aug 3, 2019 at 12:44
• $\begingroup$ @SubhashC.Davar the values in brackets are the standard errors of the estimates they are below. $\endgroup$ –  ahorn Commented Aug 4, 2019 at 10:38

Setting up null and alternative hypotheses is the first step in a t-test. You should not set them up after computing your estimates. In your specific example with income elasticity of demand, you set up the null and alternative correctly, meaning that you want the alternative hypothesis to be the statement about what you are trying to prove. You should use that null and alternative regardless of what the data then tells you.

P.S. You should report the one-sided p-value from your one-sided hypothesis test, not just the test statistic.

• $\begingroup$ What if $\hat\beta_{\ln m}=0.7$? What what your hypotheses be? How could it be intelligent to reject $\mathrm H_0$ in favour of $\mathrm H_1:\beta_{\ln m} > 1$ when clearly $0.7<1$? $\endgroup$ –  ahorn Commented Apr 30, 2019 at 4:18
• $\begingroup$ Why would you reject the null in that situation? Your new t statistic would be negative and not in the rejection region, so you would fail to reject the null. $\endgroup$ –  AlexK Commented Apr 30, 2019 at 4:48
• $\begingroup$ I now agree that the alternative hypothesis should be what I'm trying to prove. Though, it is a bit silly to do a formal hypothesis test when the estimate lies on the correct side. $\endgroup$ –  ahorn Commented May 30, 2019 at 7:33
• $\begingroup$ Here is an example of a confusing question, because the null hypothesis of elasticity and the null hypothesis of inelasticity both are accepted in those respective tests: i.sstatic.net/9zYG8.png . $\endgroup$ –  ahorn Commented May 30, 2019 at 7:35
• $\begingroup$ @ahorn Null hypothesis is typically formulated with just the $=$ sign. Then the $<$ or $>$ is used in the alternative, if the goal is to do a one-sided test. Even if the estimate is on the correct side of the alternative, it may still be statistically insignificant. With that in mind, I'm not sure what "null hypothesis of elasticity" means, because that indicates that the null hypothesis does not have an equal sign in it, which does not make sense. The image you included shows that the null of inelasticity was rejected in favor of the alternative, as the coefficient is significant. $\endgroup$ –  AlexK Commented May 30, 2019 at 8:06

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A Beginner’s Guide to Hypothesis Testing in Business

• 30 Mar 2021

Becoming a more data-driven decision-maker can bring several benefits to your organization, enabling you to identify new opportunities to pursue and threats to abate. Rather than allowing subjective thinking to guide your business strategy, backing your decisions with data can empower your company to become more innovative and, ultimately, profitable.

If you’re new to data-driven decision-making, you might be wondering how data translates into business strategy. The answer lies in generating a hypothesis and verifying or rejecting it based on what various forms of data tell you.

Below is a look at hypothesis testing and the role it plays in helping businesses become more data-driven.

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What Is Hypothesis Testing?

To understand what hypothesis testing is, it’s important first to understand what a hypothesis is.

A hypothesis or hypothesis statement seeks to explain why something has happened, or what might happen, under certain conditions. It can also be used to understand how different variables relate to each other. Hypotheses are often written as if-then statements; for example, “If this happens, then this will happen.”

Hypothesis testing , then, is a statistical means of testing an assumption stated in a hypothesis. While the specific methodology leveraged depends on the nature of the hypothesis and data available, hypothesis testing typically uses sample data to extrapolate insights about a larger population.

Hypothesis Testing in Business

When it comes to data-driven decision-making, there’s a certain amount of risk that can mislead a professional. This could be due to flawed thinking or observations, incomplete or inaccurate data , or the presence of unknown variables. The danger in this is that, if major strategic decisions are made based on flawed insights, it can lead to wasted resources, missed opportunities, and catastrophic outcomes.

The real value of hypothesis testing in business is that it allows professionals to test their theories and assumptions before putting them into action. This essentially allows an organization to verify its analysis is correct before committing resources to implement a broader strategy.

As one example, consider a company that wishes to launch a new marketing campaign to revitalize sales during a slow period. Doing so could be an incredibly expensive endeavor, depending on the campaign’s size and complexity. The company, therefore, may wish to test the campaign on a smaller scale to understand how it will perform.

In this example, the hypothesis that’s being tested would fall along the lines of: “If the company launches a new marketing campaign, then it will translate into an increase in sales.” It may even be possible to quantify how much of a lift in sales the company expects to see from the effort. Pending the results of the pilot campaign, the business would then know whether it makes sense to roll it out more broadly.

Related: 9 Fundamental Data Science Skills for Business Professionals

Key Considerations for Hypothesis Testing

1. alternative hypothesis and null hypothesis.

In hypothesis testing, the hypothesis that’s being tested is known as the alternative hypothesis . Often, it’s expressed as a correlation or statistical relationship between variables. The null hypothesis , on the other hand, is a statement that’s meant to show there’s no statistical relationship between the variables being tested. It’s typically the exact opposite of whatever is stated in the alternative hypothesis.

For example, consider a company’s leadership team that historically and reliably sees $12 million in monthly revenue. They want to understand if reducing the price of their services will attract more customers and, in turn, increase revenue.

In this case, the alternative hypothesis may take the form of a statement such as: “If we reduce the price of our flagship service by five percent, then we’ll see an increase in sales and realize revenues greater than $12 million in the next month.”

The null hypothesis, on the other hand, would indicate that revenues wouldn’t increase from the base of $12 million, or might even decrease.

Check out the video below about the difference between an alternative and a null hypothesis, and subscribe to our YouTube channel for more explainer content.

2. Significance Level and P-Value

Statistically speaking, if you were to run the same scenario 100 times, you’d likely receive somewhat different results each time. If you were to plot these results in a distribution plot, you’d see the most likely outcome is at the tallest point in the graph, with less likely outcomes falling to the right and left of that point.

With this in mind, imagine you’ve completed your hypothesis test and have your results, which indicate there may be a correlation between the variables you were testing. To understand your results' significance, you’ll need to identify a p-value for the test, which helps note how confident you are in the test results.

In statistics, the p-value depicts the probability that, assuming the null hypothesis is correct, you might still observe results that are at least as extreme as the results of your hypothesis test. The smaller the p-value, the more likely the alternative hypothesis is correct, and the greater the significance of your results.

3. One-Sided vs. Two-Sided Testing

When it’s time to test your hypothesis, it’s important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests , or one-tailed and two-tailed tests, respectively.

Typically, you’d leverage a one-sided test when you have a strong conviction about the direction of change you expect to see due to your hypothesis test. You’d leverage a two-sided test when you’re less confident in the direction of change.

4. Sampling

To perform hypothesis testing in the first place, you need to collect a sample of data to be analyzed. Depending on the question you’re seeking to answer or investigate, you might collect samples through surveys, observational studies, or experiments.

A survey involves asking a series of questions to a random population sample and recording self-reported responses.

Observational studies involve a researcher observing a sample population and collecting data as it occurs naturally, without intervention.

Finally, an experiment involves dividing a sample into multiple groups, one of which acts as the control group. For each non-control group, the variable being studied is manipulated to determine how the data collected differs from that of the control group.

Learn How to Perform Hypothesis Testing

Hypothesis testing is a complex process involving different moving pieces that can allow an organization to effectively leverage its data and inform strategic decisions.

If you’re interested in better understanding hypothesis testing and the role it can play within your organization, one option is to complete a course that focuses on the process. Doing so can lay the statistical and analytical foundation you need to succeed.

Do you want to learn more about hypothesis testing? Explore Business Analytics —one of our online business essentials courses —and download our Beginner’s Guide to Data & Analytics .

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What is Hypothesis Testing?

Hypothesis testing steps, stating the null hypothesis and alternative hypothesis, what are type i and type ii errors, hypothesis testing example, more resources, hypothesis testing.

A statistical test to support your hypothesis

Hypothesis Testing is a method of statistical inference. It is used to test if a statement regarding a population parameter is statistically significant. Hypothesis testing is a powerful tool for testing the power of predictions.

A Financial Analyst , for example, might want to make a prediction of the mean value a customer would pay for her firm’s product. She can then formulate a hypothesis, for example, “The average value that customers will pay for my product is larger than $5.” To statistically test this question, the firm owner could use hypothesis testing. This example is further explored down below.

Hypothesis Testing is a critical part of the scientific method, which is a systematic approach to assessing theories through observation. A good theory is one that can make accurate predictions. For an analyst who makes predictions, hypothesis testing is a rigorous way of backing up his prediction with statistical analysis.

Here are the steps for hypothesis testing:

• State the null hypothesis ( H 0 ) and the alternative hypothesis ( H a ).
• Consider the statistical assumptions being made. Evaluate if these assumptions are coherent with the underlying population being evaluated. For example, is assuming the underlying distribution as a normal distribution sensible?
• Determine the appropriate probability distribution and select the appropriate test statistic.
• Select the significance level commonly denoted by the Greek letter alpha (α). This is the probability threshold for which the null hypothesis will be rejected.
• Based on the significance level and on the appropriate test, state the decision rule.
• Collect the observed sample data, and use it to calculate the test statistic.
• Based on your results, you should either reject the null hypothesis or fail to reject the null hypothesis. This is known as the statistical decision.
• Consider any other economic issues that are applied to the problem. These are non-statistical considerations that need to be considered for a decision. For example, sometimes, societal cultural shifts lead to changes in consumer behavior. This must be taken into consideration in addition to the statistical decision for a final decision.

The Null Hypothesis is usually set as what we don’t want to be true. It is the hypothesis to be tested. Therefore, the Null Hypothesis is considered to be true until we have sufficient evidence to reject it. If we reject the null hypothesis, we are led to the alternative hypothesis.

Going back to our initial example of the business owner who is looking for some customer insight. Her null hypothesis would be:

H 0 : The average value customers are willing to pay for my product is smaller than or equal to $5

H 0 : µ ≤ 5

( µ = the population mean)

The alternative hypothesis would then be what we are evaluating, so, in this case, it would be:

H a : The average value customers are willing to pay for the product is greater than $5

H a : µ > 5

It is important to emphasize that the alternative hypothesis will only be considered if the sample data that we gather provide evidence for it.

The binary nature of our decision, to reject or fail to reject the null hypothesis, gives rise to two possible errors. The table below illustrates all of the possible outcomes. A Type I Error arises when a true Null Hypothesis is rejected . The probability of making a Type I Error is also known as the level of significance of the test, which is commonly referred to as alpha (α). So, for example, if a test that has its alpha set as 0.01, there is a 1% probability of rejecting a true null hypothesis or a 1% probability of making a Type I Error.

A Type II Error arises when you fail to reject a False Null Hypothesis . The probability of making a Type II Error is commonly denoted by the Greek letter beta (β). β is used to define the Power of a Test, which is the probability of correctly rejecting a false null hypothesis. The Power of a Test  is defined as 1-β . A test with more Power is more desirable, as there is a lower probability of making a Type II Error. However, there is a tradeoff between the probability of making a Type I Error and the probability of making a Type II Error.

Let’s go back to the business owner example. Let us remember the question that we are trying to answer:

Q: “Will customers pay, on average, more than $5 for our product?”

1. We have set above both the null and alternative hypothesis

2. For this example, let us assume that the firm sells organic apple juice boxes. They are consumed by a wide range of consumers of all ages, income levels, and cultural backgrounds. So, given that our product is widely used by a diverse group of consumers, assuming a normal distribution is fair.

3. Let us assume that by getting samples from our consumers, we will manage to get over 100 observations. Given we are confident with our assumption of a normal distribution for the underlying population and have a large number of observations, we will use a z-test.

4. We want to be confident of our result, so let us pick our significance level as α = 5%. This will provide strong evidence of our result.

5. We are using a z-test with a significance level, and the null hypothesis is  µ ≤ 5, so our rejection point will be  z 0.05  =1.645 . This means that if the z score calculated from our sample is greater than 1.645, we reject the null hypothesis. 

6. Now assume that we have collected our data and that from our sample of 100 observations, the mean price that customers are willing to pay for our juices is $5.02  and that the sample standard deviation was $0.10 . We can now calculate the z-score for our sample where we get a value of 2 given by  [(5.02 – 5) / ( 0.1/  √ 100)].

7. Given our calculated z is greater than  z 0.05  =1.645,  we have strong evidence to reject the null hypothesis at a 5% significance level. We are then in favor of the alternative hypothesis that t he average value customers are willing to pay for the product is greater than $5. 

8. We now need to take into consideration any economic or qualitative issues that are not addressed through the statistical process. These are usually non-quantifiable variables that have to be addressed when making a decision based on the findings. For example, if the biggest competitor was going to lower the price of the competing product significantly, that may lower the average value consumers are willing to pay for your product.

If you want to learn more about topics related to Hypothesis Testing, check out resources on the Royal Statistics Society website . To keep learning and advancing your career, the following CFI resources will also be helpful:

• Delphi Method
• Cointegration
• Durbin Watson Statistic
• Fibonacci Numbers
• AVERAGE Excel Function
• See all data science resources
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Hypothesis Testing

Hypothesis testing is a tool for making statistical inferences about the population data. It is an analysis tool that tests assumptions and determines how likely something is within a given standard of accuracy. Hypothesis testing provides a way to verify whether the results of an experiment are valid.

A null hypothesis and an alternative hypothesis are set up before performing the hypothesis testing. This helps to arrive at a conclusion regarding the sample obtained from the population. In this article, we will learn more about hypothesis testing, its types, steps to perform the testing, and associated examples.

What is Hypothesis Testing in Statistics?

Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution . It tests an assumption made about the data using different types of hypothesis testing methodologies. The hypothesis testing results in either rejecting or not rejecting the null hypothesis.

Hypothesis Testing Definition

Hypothesis testing can be defined as a statistical tool that is used to identify if the results of an experiment are meaningful or not. It involves setting up a null hypothesis and an alternative hypothesis. These two hypotheses will always be mutually exclusive. This means that if the null hypothesis is true then the alternative hypothesis is false and vice versa. An example of hypothesis testing is setting up a test to check if a new medicine works on a disease in a more efficient manner.

Null Hypothesis

The null hypothesis is a concise mathematical statement that is used to indicate that there is no difference between two possibilities. In other words, there is no difference between certain characteristics of data. This hypothesis assumes that the outcomes of an experiment are based on chance alone. It is denoted as \(H_{0}\). Hypothesis testing is used to conclude if the null hypothesis can be rejected or not. Suppose an experiment is conducted to check if girls are shorter than boys at the age of 5. The null hypothesis will say that they are the same height.

Alternative Hypothesis

The alternative hypothesis is an alternative to the null hypothesis. It is used to show that the observations of an experiment are due to some real effect. It indicates that there is a statistical significance between two possible outcomes and can be denoted as \(H_{1}\) or \(H_{a}\). For the above-mentioned example, the alternative hypothesis would be that girls are shorter than boys at the age of 5.

Hypothesis Testing P Value

In hypothesis testing, the p value is used to indicate whether the results obtained after conducting a test are statistically significant or not. It also indicates the probability of making an error in rejecting or not rejecting the null hypothesis.This value is always a number between 0 and 1. The p value is compared to an alpha level, \(\alpha\) or significance level. The alpha level can be defined as the acceptable risk of incorrectly rejecting the null hypothesis. The alpha level is usually chosen between 1% to 5%.

Hypothesis Testing Critical region

All sets of values that lead to rejecting the null hypothesis lie in the critical region. Furthermore, the value that separates the critical region from the non-critical region is known as the critical value.

Hypothesis Testing Formula

Depending upon the type of data available and the size, different types of hypothesis testing are used to determine whether the null hypothesis can be rejected or not. The hypothesis testing formula for some important test statistics are given below:

• z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\). \(\overline{x}\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the population standard deviation and n is the size of the sample.
• t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\). s is the sample standard deviation.
• \(\chi ^{2} = \sum \frac{(O_{i}-E_{i})^{2}}{E_{i}}\). \(O_{i}\) is the observed value and \(E_{i}\) is the expected value.

We will learn more about these test statistics in the upcoming section.

Types of Hypothesis Testing

Selecting the correct test for performing hypothesis testing can be confusing. These tests are used to determine a test statistic on the basis of which the null hypothesis can either be rejected or not rejected. Some of the important tests used for hypothesis testing are given below.

Hypothesis Testing Z Test

A z test is a way of hypothesis testing that is used for a large sample size (n ≥ 30). It is used to determine whether there is a difference between the population mean and the sample mean when the population standard deviation is known. It can also be used to compare the mean of two samples. It is used to compute the z test statistic. The formulas are given as follows:

• One sample: z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).
• Two samples: z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).

Hypothesis Testing t Test

The t test is another method of hypothesis testing that is used for a small sample size (n < 30). It is also used to compare the sample mean and population mean. However, the population standard deviation is not known. Instead, the sample standard deviation is known. The mean of two samples can also be compared using the t test.

• One sample: t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\).
• Two samples: t = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}\).

Hypothesis Testing Chi Square

The Chi square test is a hypothesis testing method that is used to check whether the variables in a population are independent or not. It is used when the test statistic is chi-squared distributed.

One Tailed Hypothesis Testing

One tailed hypothesis testing is done when the rejection region is only in one direction. It can also be known as directional hypothesis testing because the effects can be tested in one direction only. This type of testing is further classified into the right tailed test and left tailed test.

Right Tailed Hypothesis Testing

The right tail test is also known as the upper tail test. This test is used to check whether the population parameter is greater than some value. The null and alternative hypotheses for this test are given as follows:

\(H_{0}\): The population parameter is ≤ some value

\(H_{1}\): The population parameter is > some value.

If the test statistic has a greater value than the critical value then the null hypothesis is rejected

Left Tailed Hypothesis Testing

The left tail test is also known as the lower tail test. It is used to check whether the population parameter is less than some value. The hypotheses for this hypothesis testing can be written as follows:

\(H_{0}\): The population parameter is ≥ some value

\(H_{1}\): The population parameter is < some value.

The null hypothesis is rejected if the test statistic has a value lesser than the critical value.

Two Tailed Hypothesis Testing

In this hypothesis testing method, the critical region lies on both sides of the sampling distribution. It is also known as a non - directional hypothesis testing method. The two-tailed test is used when it needs to be determined if the population parameter is assumed to be different than some value. The hypotheses can be set up as follows:

\(H_{0}\): the population parameter = some value

\(H_{1}\): the population parameter ≠ some value

The null hypothesis is rejected if the test statistic has a value that is not equal to the critical value.

Hypothesis Testing Steps

Hypothesis testing can be easily performed in five simple steps. The most important step is to correctly set up the hypotheses and identify the right method for hypothesis testing. The basic steps to perform hypothesis testing are as follows:

• Step 1: Set up the null hypothesis by correctly identifying whether it is the left-tailed, right-tailed, or two-tailed hypothesis testing.
• Step 2: Set up the alternative hypothesis.
• Step 3: Choose the correct significance level, \(\alpha\), and find the critical value.
• Step 4: Calculate the correct test statistic (z, t or \(\chi\)) and p-value.
• Step 5: Compare the test statistic with the critical value or compare the p-value with \(\alpha\) to arrive at a conclusion. In other words, decide if the null hypothesis is to be rejected or not.

Hypothesis Testing Example

The best way to solve a problem on hypothesis testing is by applying the 5 steps mentioned in the previous section. Suppose a researcher claims that the mean average weight of men is greater than 100kgs with a standard deviation of 15kgs. 30 men are chosen with an average weight of 112.5 Kgs. Using hypothesis testing, check if there is enough evidence to support the researcher's claim. The confidence interval is given as 95%.

Step 1: This is an example of a right-tailed test. Set up the null hypothesis as \(H_{0}\): \(\mu\) = 100.

Step 2: The alternative hypothesis is given by \(H_{1}\): \(\mu\) > 100.

Step 3: As this is a one-tailed test, \(\alpha\) = 100% - 95% = 5%. This can be used to determine the critical value.

1 - \(\alpha\) = 1 - 0.05 = 0.95

0.95 gives the required area under the curve. Now using a normal distribution table, the area 0.95 is at z = 1.645. A similar process can be followed for a t-test. The only additional requirement is to calculate the degrees of freedom given by n - 1.

Step 4: Calculate the z test statistic. This is because the sample size is 30. Furthermore, the sample and population means are known along with the standard deviation.

z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\).

\(\mu\) = 100, \(\overline{x}\) = 112.5, n = 30, \(\sigma\) = 15

z = \(\frac{112.5-100}{\frac{15}{\sqrt{30}}}\) = 4.56

Step 5: Conclusion. As 4.56 > 1.645 thus, the null hypothesis can be rejected.

Hypothesis Testing and Confidence Intervals

Confidence intervals form an important part of hypothesis testing. This is because the alpha level can be determined from a given confidence interval. Suppose a confidence interval is given as 95%. Subtract the confidence interval from 100%. This gives 100 - 95 = 5% or 0.05. This is the alpha value of a one-tailed hypothesis testing. To obtain the alpha value for a two-tailed hypothesis testing, divide this value by 2. This gives 0.05 / 2 = 0.025.

Related Articles:

• Probability and Statistics
• Data Handling

Important Notes on Hypothesis Testing

• Hypothesis testing is a technique that is used to verify whether the results of an experiment are statistically significant.
• It involves the setting up of a null hypothesis and an alternate hypothesis.
• There are three types of tests that can be conducted under hypothesis testing - z test, t test, and chi square test.
• Hypothesis testing can be classified as right tail, left tail, and two tail tests.

Examples on Hypothesis Testing

• Example 1: The average weight of a dumbbell in a gym is 90lbs. However, a physical trainer believes that the average weight might be higher. A random sample of 5 dumbbells with an average weight of 110lbs and a standard deviation of 18lbs. Using hypothesis testing check if the physical trainer's claim can be supported for a 95% confidence level. Solution: As the sample size is lesser than 30, the t-test is used. \(H_{0}\): \(\mu\) = 90, \(H_{1}\): \(\mu\) > 90 \(\overline{x}\) = 110, \(\mu\) = 90, n = 5, s = 18. \(\alpha\) = 0.05 Using the t-distribution table, the critical value is 2.132 t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\) t = 2.484 As 2.484 > 2.132, the null hypothesis is rejected. Answer: The average weight of the dumbbells may be greater than 90lbs
• Example 2: The average score on a test is 80 with a standard deviation of 10. With a new teaching curriculum introduced it is believed that this score will change. On random testing, the score of 38 students, the mean was found to be 88. With a 0.05 significance level, is there any evidence to support this claim? Solution: This is an example of two-tail hypothesis testing. The z test will be used. \(H_{0}\): \(\mu\) = 80, \(H_{1}\): \(\mu\) ≠ 80 \(\overline{x}\) = 88, \(\mu\) = 80, n = 36, \(\sigma\) = 10. \(\alpha\) = 0.05 / 2 = 0.025 The critical value using the normal distribution table is 1.96 z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) z = \(\frac{88-80}{\frac{10}{\sqrt{36}}}\) = 4.8 As 4.8 > 1.96, the null hypothesis is rejected. Answer: There is a difference in the scores after the new curriculum was introduced.
• Example 3: The average score of a class is 90. However, a teacher believes that the average score might be lower. The scores of 6 students were randomly measured. The mean was 82 with a standard deviation of 18. With a 0.05 significance level use hypothesis testing to check if this claim is true. Solution: The t test will be used. \(H_{0}\): \(\mu\) = 90, \(H_{1}\): \(\mu\) < 90 \(\overline{x}\) = 110, \(\mu\) = 90, n = 6, s = 18 The critical value from the t table is -2.015 t = \(\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}\) t = \(\frac{82-90}{\frac{18}{\sqrt{6}}}\) t = -1.088 As -1.088 > -2.015, we fail to reject the null hypothesis. Answer: There is not enough evidence to support the claim.

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FAQs on Hypothesis Testing

What is hypothesis testing.

Hypothesis testing in statistics is a tool that is used to make inferences about the population data. It is also used to check if the results of an experiment are valid.

What is the z Test in Hypothesis Testing?

The z test in hypothesis testing is used to find the z test statistic for normally distributed data . The z test is used when the standard deviation of the population is known and the sample size is greater than or equal to 30.

What is the t Test in Hypothesis Testing?

The t test in hypothesis testing is used when the data follows a student t distribution . It is used when the sample size is less than 30 and standard deviation of the population is not known.

What is the formula for z test in Hypothesis Testing?

The formula for a one sample z test in hypothesis testing is z = \(\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\) and for two samples is z = \(\frac{(\overline{x_{1}}-\overline{x_{2}})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}}\).

What is the p Value in Hypothesis Testing?

The p value helps to determine if the test results are statistically significant or not. In hypothesis testing, the null hypothesis can either be rejected or not rejected based on the comparison between the p value and the alpha level.

What is One Tail Hypothesis Testing?

When the rejection region is only on one side of the distribution curve then it is known as one tail hypothesis testing. The right tail test and the left tail test are two types of directional hypothesis testing.

What is the Alpha Level in Two Tail Hypothesis Testing?

To get the alpha level in a two tail hypothesis testing divide \(\alpha\) by 2. This is done as there are two rejection regions in the curve.

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What Is Hypothesis Testing?

Step 1: define the hypothesis, step 2: set the criteria, step 3: calculate the statistic, step 4: reach a conclusion, types of errors, the bottom line.

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Hypothesis Testing in Finance: Concept and Examples

Charlene Rhinehart is a CPA , CFE, chair of an Illinois CPA Society committee, and has a degree in accounting and finance from DePaul University.

Your investment advisor proposes you a monthly income investment plan that promises a variable return each month. You will invest in it only if you are assured of an average $180 monthly income. Your advisor also tells you that for the past 300 months, the scheme had investment returns with an average value of $190 and a standard deviation of $75. Should you invest in this scheme? Hypothesis testing comes to the aid for such decision-making.

Key Takeaways

• Hypothesis testing is a mathematical tool for confirming a financial or business claim or idea.
• Hypothesis testing is useful for investors trying to decide what to invest in and whether the instrument is likely to provide a satisfactory return.
• Despite the existence of different methodologies of hypothesis testing, the same four steps are used: define the hypothesis, set the criteria, calculate the statistic, and reach a conclusion.
• This mathematical model, like most statistical tools and models, has limitations and is prone to certain errors, necessitating investors also considering other models in conjunction with this one

Hypothesis or significance testing is a mathematical model for testing a claim, idea or hypothesis about a parameter of interest in a given population set, using data measured in a sample set. Calculations are performed on selected samples to gather more decisive information about the characteristics of the entire population, which enables a systematic way to test claims or ideas about the entire dataset.

Here is a simple example: A school principal reports that students in their school score an average of 7 out of 10 in exams. To test this “hypothesis,” we record marks of say 30 students (sample) from the entire student population of the school (say 300) and calculate the mean of that sample. We can then compare the (calculated) sample mean to the (reported) population mean and attempt to confirm the hypothesis.

To take another example, the annual return of a particular mutual fund is 8%. Assume that mutual fund has been in existence for 20 years. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate its mean. We then compare the (calculated) sample mean to the (claimed) population mean to verify the hypothesis.

This article assumes readers' familiarity with concepts of a normal distribution table, formula, p-value and related basics of statistics.

Different methodologies exist for hypothesis testing, but the same four basic steps are involved:

Usually, the reported value (or the claim statistics) is stated as the hypothesis and presumed to be true. For the above examples, the hypothesis will be:

• Example A: Students in the school score an average of 7 out of 10 in exams.
• Example B: The annual return of the mutual fund is 8% per annum.

This stated description constitutes the “ Null Hypothesis (H 0 ) ” and is  assumed  to be true – the way a defendant in a jury trial is presumed innocent until proven guilty by the evidence presented in court. Similarly, hypothesis testing starts by stating and assuming a “ null hypothesis ,” and then the process determines whether the assumption is likely to be true or false.

The important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the  Alternative Hypothesis (H 1 ).  For the above examples, the alternative hypothesis will be:

• Students score an average that is not equal to 7.
• The annual return of the mutual fund is not equal to 8% per annum.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

As in a trial, the jury assumes the defendant's innocence (null hypothesis). The prosecutor has to prove otherwise (alternative hypothesis). Similarly, the researcher has to prove that the null hypothesis is either true or false. If the prosecutor fails to prove the alternative hypothesis, the jury has to let the defendant go (basing the decision on the null hypothesis). Similarly, if the researcher fails to prove an alternative hypothesis (or simply does nothing), then the null hypothesis is assumed to be true.

The decision-making criteria have to be based on certain parameters of datasets.

The decision-making criteria have to be based on certain parameters of datasets and this is where the connection to normal distribution comes into the picture.

As per the standard statistics postulate about sampling distribution , for any sample size n, the sampling distribution of X is normal if the X from which the sample is drawn is normally distributed. Hence, the probabilities of all other possible sample mean that one could select are normally distributed.

For e.g., determine if the average daily return, of any stock listed on XYZ stock market , around New Year's Day is greater than 2%.

H 0 : Null Hypothesis: mean = 2%

H 1 : Alternative Hypothesis: mean > 2% (this is what we want to prove)

Take the sample (say of 50 stocks out of total 500) and compute the mean of the sample.

For a normal distribution, 95% of the values lie within two standard deviations of the population mean. Hence, this normal distribution and central limit assumption for the sample dataset allows us to establish 5% as a significance level. It makes sense as, under this assumption, there is less than a 5% probability (100-95) of getting outliers that are beyond two standard deviations from the population mean. Depending upon the nature of datasets, other significance levels can be taken at 1%, 5% or 10%. For financial calculations (including behavioral finance), 5% is the generally accepted limit. If we find any calculations that go beyond the usual two standard deviations, then we have a strong case of outliers to reject the null hypothesis.  

Graphically, it is represented as follows:

In the above example, if the mean of the sample is much larger than 2% (say 3.5%), then we reject the null hypothesis. The alternative hypothesis (mean >2%) is accepted, which confirms that the average daily return of the stocks is indeed above 2%.

However, if the mean of the sample is not likely to be significantly greater than 2% (and remains at, say, around 2.2%), then we CANNOT reject the null hypothesis. The challenge comes on how to decide on such close range cases. To make a conclusion from selected samples and results, a level of significance is to be determined, which enables a conclusion to be made about the null hypothesis. The alternative hypothesis enables establishing the level of significance or the "critical value” concept for deciding on such close range cases.

According to the textbook standard definition, “A critical value is a cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means obtained beyond a critical value will result in a decision to reject the null hypothesis." In the above example, if we have defined the critical value as 2.1%, and the calculated mean comes to 2.2%, then we reject the null hypothesis. A critical value establishes a clear demarcation about acceptance or rejection.

This step involves calculating the required figure(s), known as test statistics (like mean, z-score , p-value , etc.), for the selected sample. (We'll get to these in a later section.)

With the computed value(s), decide on the null hypothesis. If the probability of getting a sample mean is less than 5%, then the conclusion is to reject the null hypothesis. Otherwise, accept and retain the null hypothesis.

There can be four possible outcomes in sample-based decision-making, with regard to the correct applicability to the entire population:

The “Correct” cases are the ones where the decisions taken on the samples are truly applicable to the entire population. The cases of errors arise when one decides to retain (or reject) the null hypothesis based on the sample calculations, but that decision does not really apply for the entire population. These cases constitute Type 1 ( alpha ) and Type 2 ( beta ) errors, as indicated in the table above.

Selecting the correct critical value allows eliminating the type-1 alpha errors or limiting them to an acceptable range.

Alpha denotes the error on the level of significance and is determined by the researcher. To maintain the standard 5% significance or confidence level for probability calculations, this is retained at 5%.

According to the applicable decision-making benchmarks and definitions:

• “This (alpha) criterion is usually set at 0.05 (a = 0.05), and we compare the alpha level to the p-value. When the probability of a Type I error is less than 5% (p < 0.05), we decide to reject the null hypothesis; otherwise, we retain the null hypothesis.”
• The technical term used for this probability is the p-value . It is defined as “the probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true. The p-value for obtaining a sample outcome is compared to the level of significance."
• A Type II error, or beta error, is defined as the probability of incorrectly retaining the null hypothesis, when in fact it is not applicable to the entire population.

A few more examples will demonstrate this and other calculations.

A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if they are assured of an average $180 monthly income. The investor has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should they invest in this scheme?

Let’s set up the problem. The investor will invest in the scheme if they are assured of the investor's desired $180 average return.

H 0 : Null Hypothesis: mean = 180

H 1 : Alternative Hypothesis: mean > 180

Method 1: Critical Value Approach

Identify a critical value X L for the sample mean, which is large enough to reject the null hypothesis – i.e. reject the null hypothesis if the sample mean >= critical value X L

P (identify a Type I alpha error) = P (reject H 0  given that H 0  is true),

This would be achieved when the sample mean exceeds the critical limits.

= P (given that H 0  is true) = alpha

Graphically, it appears as follows:

Taking alpha = 0.05 (i.e. 5% significance level), Z 0.05  = 1.645 (from the Z-table or normal distribution table)

           = > X L  = 180 +1.645*(75/sqrt(300)) = 187.12

Since the sample mean (190) is greater than the critical value (187.12), the null hypothesis is rejected, and the conclusion is that the average monthly return is indeed greater than $180, so the investor can consider investing in this scheme.

Method 2: Using Standardized Test Statistics

One can also use standardized value z.

Test Statistic, Z = (sample mean – population mean) / (std-dev / sqrt (no. of samples).

Then, the rejection region becomes the following:

Z= (190 – 180) / (75 / sqrt (300)) = 2.309

Our rejection region at 5% significance level is Z> Z 0.05  = 1.645.

Since Z= 2.309 is greater than 1.645, the null hypothesis can be rejected with a similar conclusion mentioned above.

Method 3: P-value Calculation

We aim to identify P (sample mean >= 190, when mean = 180).

= P (Z >= (190- 180) / (75 / sqrt (300))

= P (Z >= 2.309) = 0.0084 = 0.84%

The following table to infer p-value calculations concludes that there is confirmed evidence of average monthly returns being higher than 180:

A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively.

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

H 0 : Null Hypothesis: mean = 18

H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)

Rejection region: Z <= - Z 2.5  and Z>=Z 2.5  (assuming 5% significance level, split 2.5 each on either side).

Z = (sample mean – mean) / (std-dev / sqrt (no. of samples))

= (18.75 – 18) / (6/(sqrt(100)) = 1.25

This calculated Z value falls between the two limits defined by:

- Z 2.5  = -1.96 and Z 2.5  = 1.96.

This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker.

Alternatively, The p-value = P(Z< -1.25)+P(Z >1.25)

= 2 * 0.1056 = 0.2112 = 21.12% which is greater than 0.05 or 5%, leading to the same conclusion.

Graphically, it is represented by the following:

Criticism Points for the Hypothetical Testing Method:

• A statistical method based on assumptions
• Error-prone as detailed in terms of alpha and beta errors
• Interpretation of p-value can be ambiguous, leading to confusing results

Hypothesis testing allows a mathematical model to validate a claim or idea with a certain confidence level. However, like the majority of statistical tools and models, it is bound by a few limitations. The use of this model for making financial decisions should be considered with a critical eye, keeping all dependencies in mind. Alternate methods like  Bayesian Inference are also worth exploring for similar analysis.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 4-5.

Rice University, OpenStax. " Introductory Statistics 2e: 7.1 The Central Limit Theorem for Sample Means (Averages) ."

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 5-6.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 13.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 6.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 6-7.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 10.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 11.

Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 7, 10-11.

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Value Hypothesis Fundamentals: A Complete Guide

Last updated on Fri Aug 23 2024

Imagine spending months or even years developing a new feature only to find out it doesn’t resonate with your users, argh! This kind of situation could be any worst Product manager’s nightmare.

There's a way to fix this problem called the Value Hypothesis . This idea helps builders to validate whether the ideas they’re working on are worth pursuing and useful to the people they want to sell to.

This guide will teach you what you need to know about Value Hypothesis and a step-by-step process on how to create a strong one. At the end of this post, you’ll learn how to create a product that satisfies your users.

Are you ready? Let’s get to it!

How a Value Hypothesis Helps Product Managers

Scrutinizing this hypothesis helps you as a developer to come up with a product that your customers like and love to use.

Product managers use the Value Hypothesis as a north star, ensuring focus on client needs and avoiding wasted resources. For more on this, read about the product management process .

Definition and Scope of Value Hypothesis

Let's get into the step-by-step process, but first, we need to understand the basics of the Value Hypothesis:

What Is a Value Hypothesis?

A Value Hypothesis is like a smart guess you can test to see if your product truly solves a problem for your customers. It’s your way of predicting how well your product will address a particular issue for the people you’re trying to help.

You need to know what a Value Hypothesis is, what it covers, and its key parts before you use it. To learn more about finding out what customers need, take a look at our guide on discovering features .

The Value Hypothesis does more than just help with the initial launch, it guides the whole development process. This keeps teams focused on what their users care about helping them choose features that their audience will like.

Critical Components of a Value Hypothesis

A strong Value Hypothesis rests on three key components:

Value Proposition: The Value Proposition spells out the main advantage your product gives to customers. It explains the "what" and "why" of your product showing how it eases a particular pain point.

This proposition targets a specific group of consumers. To learn more, check out our guide on roadmapping .

Customer Segmentation: Knowing and grasping your target audience is essential. This involves studying their demographics, needs, behaviors, and problems. By dividing your market, you can shape your value proposition to address the unique needs of each group.

Customer feedback surveys can prove priceless in this process. Find out more about this in our customer feedback surveys guide.

Problem Statement : The Problem Statement defines the exact issue your product aims to fix. It should zero in on a real fixable pain point your target users face. For hands-on applications, see our product launch communication plan .

Here are some key questions to guide you:

What are the primary challenges and obstacles faced by your target users?

What existing solutions are available, and where do they fall short?

What unmet needs or desires does your target audience have?

For a structured approach to prioritizing features based on customer needs, consider using a feature prioritization matrix .

Crafting a Strong Value Hypothesis

Now that we've covered the basics, let's look at how to build a convincing Value Hypothesis. Here's a two-step method, along with value hypothesis templates, to point you in the right direction:

1. Research and Analysis

To start with, you need to carry out market research. By carrying out proper market research, you will have an understanding of existing solutions and identify areas in which customers' needs are yet to be met. This is integral to effective idea tracking .

Next, use customer interviews, surveys, and support data to understand your target audience's problems and what they want. Check out our list of tools for getting customer feedback to help with this.

2. Finding Out What Customers Need

Once you've completed your research, it's crucial to identify your customers' needs. By merging insights from market research with direct user feedback, you can pinpoint the key requirements of your customers.

Here are some key questions to think about:

What are the most significant challenges that your target users encounter daily?

Which current solutions are available to them, and how do these solutions fail to fully address their needs?

What specific pain points are your target users struggling with that aren't being resolved?

Are there any gaps or shortcomings in the existing products or services that your customers use?

What unfulfilled needs or desires does your target audience express that aren't currently met by the market?

To prioritize features based on customer needs in a structured way, think about using a feature prioritization matrix .

Validating the Value Hypothesis

Once you've created your Value Hypothesis with a template, you need to check if it holds up. Here's how you can do this:

MVP Testing

Build a minimum viable product (MVP)—a basic version of your product with essential functions. This lets you test your value proposition with actual users and get feedback without spending too much. To achieve the best outcomes, look into the best practices for customer feedback software .

Prototyping

Build mock-ups to show your product idea. Use these mock-ups to get user input on the user experience and overall value offer.

Metrics for Evaluation

After you've gathered data about your hypothesis, it's time to examine it. Here are some metrics you can use:

User Engagement : Monitor stats like time on the platform, feature use, and return visits to see how much users interact with your MVP or mock-up.

Conversion Rates : Check conversion rates for key actions like sign-ups, buys, or feature adoption. These numbers help you judge if your value offer clicks with users. To learn more, read our article on SaaS growth benchmarks .

Iterative Improvement of Value Hypothesis

The Value Hypothesis framework shines because you can keep making it better. Here's how to fine-tune your hypothesis:

Set up an ongoing system to gather user data as you develop your product.

Look at what users say to spot areas that need work then update your value proposition based on what you learn.

Read about managing product updates to keep your hypotheses current.

Adaptation to Market Changes

The market keeps changing, and your Value Hypothesis should too. Stay up to date on what's happening in your industry and watch how users' habits change. Tweak your value proposition to stay useful and ahead of the competition.

Here are some ways to keep your Value Hypothesis fresh:

Do market research often to keep up with what's happening in your industry and what your competitors are up to.

Keep an eye on what users are saying to spot new problems or things they need but don't have yet.

Try out different value statements and features to see which ones your audience likes best.

To keep your guesses up-to-date, check out our guide on handling product changes .

Common Mistakes to Avoid

While the Value Hypothesis approach is powerful, it's key to steer clear of these common traps:

Avoid Confirmation Bias : People tend to focus on data that backs up their initial guesses. But it's key to look at feedback that goes against your ideas and stay open to different views.

Watch out for Shiny Object Syndrome : Don't let the newest fads sway you unless they solve a main customer problem. Your value proposition should fix actual issues for your users.

Don't Cling to Your First Hypothesis : As the market changes, your value proposition should too. Be ready to shift your hypothesis when new evidence and user feedback comes in.

Don't Mix Up Busywork with Real Progress : Getting user feedback is key, but making sense of it brings real value. Look at the data to find useful insights that can shape your product. To learn more about this, check out our guide on handling customer feedback .

Value Hypothesis: Action Points

To build a product that succeeds, you need to know your target users inside out and understand how you help them. The Value Hypothesis framework gives you a step-by-step way to do this.

If you follow the steps in this guide, you can create a strong value proposition, check if it works, and keep improving it to ensure your product stays useful and important to your customers.

Keep in mind, a good Value Hypothesis changes as your product and market change. When you use data and put customers first, you're on the right track to create a product that works.

Want to put the Value Hypothesis framework into action? Check out our top templates for creating product roadmaps to streamline your process. Think about using featureOS to manage customer feedback. This tool makes it easier to collect, examine, and put user feedback to work.

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