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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 ).

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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Chapter 8 Introduction to Hypothesis Testing

Sep 22, 2014

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Chapter 8 Introduction to Hypothesis Testing. PowerPoint Lecture Slides Essentials of Statistics for the Behavioral Sciences Seventh Edition by Frederick J. Gravetter and Larry B. Wallnau. Chapter 8 Learning Outcomes. Concepts to review. z- Scores (Chapter 5)

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Chapter 8 Introduction to Hypothesis Testing PowerPoint Lecture SlidesEssentials of Statistics for the Behavioral SciencesSeventh Editionby Frederick J. Gravetter and Larry B. Wallnau

Chapter 8 Learning Outcomes

Concepts to review • z-Scores (Chapter 5) • Distribution of sample means (Chapter 7) • Expected value • Standard error • Probability and sample means

8.1 Logic of Hypothesis Testing • Hypothesis testing is one of the most commonly used inferential procedures • Definition: a statistical method that uses sample data to evaluate a hypothesis about a population

Logic of hypothesis test • State hypothesis about a population • Predict the characteristics of the sample based on the hypothesis • Obtain a random sample from the population • Compare the obtained sample data with the prediction made from the hypothesis • If consistent, hypothesis is reasonable • If discrepant, hypothesis is rejected

Figure 8.1 Basic experimental situation

Figure 8.2 Unknown population in experimental situation

Four steps of Hypothesis Testing • State the hypotheses • Set the criteria for a decision • Collect data and compute sample statistics • Make a decision

Step 1: State hypotheses • Null hypothesis (H0) states that, in the general population, there is no change, no difference, or not relationship • Alternative hypothesis (H1) states that there is a change, a difference, or a relationship in the general population

Step 2: Set the criteria for decision • Distribution of sample means is divided • Those likely if H0 is true • Those very unlikely if H0 is true • Alpha level, or level of significance, is a probability value used to define “very unlikely” • Critical region is composed of the extreme sample values that are very unlikely • Boundaries of critical region are determined by alpha level.

Figure 8.3 Division of distribution of sample means

Figure 8.4 Critical regions for α = .05

Learning Check • A sports coach is investigating the impact of a new training method. In words, what would the null hypothesis say?

Learning Check - Answer • A sports coach is investigating the impact of a new training method. In words, what would the null hypothesis say?

Learning Check • Decide if each of the following statements is True or False.

Step 3: Collect data and Compute sample statistics • Data collected after hypotheses stated • Data collected after criteria for decision set • This sequence assures objectivity • Compute a sample statistic (z-score) to show the exact position of the sample.

Step 4: Make a decision • If sample data are in the critical region, the null hypothesis is rejected • If the sample data are not in the critical region, the researcher fails to reject the null hypothesis

Box 8.1: Proving the alternative hypothesis • Seems odd to focus on null hypothesis, which we do not believe to be true. • In logic, it is easier to demonstrate that a universal hypothesis is false than true.

Jury trial: an analogy • Trial begins with null hypothesis (innocent until proven guilty). • Police and prosecutor gather evidence (data) to show reject innocent plea and conclude guilt. • If there is sufficient evidence, jury rejects innocence claim and concludes guilt. • If there is not enough evidence, jury fails to convict (but does not conclude defendant is innocent).

8.2 Uncertainty and Errors in Hypothesis Testing • Hypothesis testing is an inferential process • Uses limited information to reach general conclusion • Sample data used to draw conclusion about a population • Errors are possible

Type I Errors • Researcher rejects a null hypothesis that is actually true • Researcher concludes that a treatment has an effect when it has none • Alpha level is the probability that a test will lead to a Type I error.

Type II Errors • Researcher fails to reject a null hypothesis that is really false. • Researcher has failed to detect a real treatment effect.

Figure 8.5 Location of critical region boundaries

Learning Check TF • Decide if each of the following statements is True or False.

8.3 Example of a Hypothesis Test • Step 1: H0: alcohol exposure =18 (Even with alcohol exposure, the rats still average 18 grams at birth.) • Step 2: α = .05Critical region: z beyond ±1.96 • Step 3: z = 3.00 • Step 4: Reject H0

Figure 8.6 Structure of study in example

Figure 8.7 Critical region for Example 8.2

In the Literature • A result is significant or statistically significant if it is very unlikely to occur when the null hypothesis is true. • In APA format • State significance • Report value of test statistic • Report alpha level or p-value

Factors influencing hypothesis test • Size of difference between sample mean and original population mean • Appears in numerator of the z-score • Variability of the scores • Influences size of the standard error • Number of scores in the sample • Influences size of the standard error

Assumptions for hypothesis tests • Random sampling • Independent observations • Value of standard deviation is unchanged by the treatment • Normal sampling distribution

Figure 8.8 Rejection / critical region

Learning Check • A researcher uses a hypothesis test to evaluate H0 µ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis?

Learning Check - Answer • A researcher uses a hypothesis test to evaluate H0 µ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis?

8.4 Directional (One-Tailed) Hypothesis Tests • The procedure in Section 8.3 is two-tailed because critical region is divided on both tails of the distribution. • Researchers usually have a specific prediction about the direction of a treatment effect before they begin. • In a directional hypothesis or one-tailed test, the hypotheses specify an increase or decrease in the population mean

Figure 8.9 Critical region for Example 8.3

Learning Check • A researcher is predicting that a treatment will decrease scores. If this treatment is evaluated using a directional hypothesis test, then the critical region for the test

8.5 Concerns about Hypothesis Testing: Measuring Effect Size • Although commonly used, some researchers are concerned about hypothesis testing • Focus of test is data, not hypothesis • Significant effects are not always substantial • Effect size measures the absolute magnitude of a treatment effect, independent of sample size

Cohen’s d : measure of effect size

Figure 8.10 A 15-point difference in two situations

8.6 Statistical Power • The power of a test is the probability that the test will correctly reject a false null hypothesis • It will detect a treatment effect if one exists • Power = 1 – β or 1 – p (Type II error) • Power usually computed before starting study • Requires assumptions about factors that influence power

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TESTING HYPOTHESIS IN RESEARCH

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Formulation of hypothesis and testing

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