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Outbyte Driver Updater FREEFix the driver behind crashes, sound loss and screen glitchesFind Drivers →Outbyte PC Repair FREEClear out junk files and repair common Windows errorsFree Scan →Hypothesis testing uses sample data to evaluate a claim about a population. The seven-step diagram below separates the process into planning, calculation and interpretation; it is a useful teaching sequence, not the only accepted way to count the steps.
The seven steps at a glance
| Step | What you do | Key question |
|---|---|---|
| 1. Frame the research question | Identify the population and the parameter you want to learn about. | What population quantity is at issue? |
| 2. State the hypotheses | Write the null hypothesis, H₀, and alternative hypothesis, Hₐ, in terms of the population parameter. | What claim is tested, and what result would count as evidence against it? |
| 3. Check the design and test conditions | Confirm that the study design and data meet the assumptions of the chosen test. | Are the observations and sampling conditions suitable for this test? |
| 4. Choose the significance level, α | Set the decision threshold before evaluating the results. | What Type I error risk is acceptable for this procedure? |
| 5. Calculate the test statistic | Use the sample data and chosen test to summarize how unusual the result is under H₀. | How far is the observed result from what H₀ predicts? |
| 6. Find the p-value or rejection region | Compare the result with the null model using a p-value, or compare the statistic with a critical value. | Does the result meet the decision rule? |
| 7. Decide and explain | Reject H₀ or fail to reject H₀, then interpret the decision in the context of the question. | What does the evidence say about the original claim? |
1. Frame the research question
Begin by specifying the population and the quantity of interest, such as a population mean, proportion or difference. A statistical hypothesis is a statement about that population parameter—not merely a description of the sample you happened to observe.
For example, “Is the average adult body temperature 98.6 degrees, or is it lower?” is a question about a population average. The number in this example is part of the question, not a newly established finding.
2. State H₀ and Hₐ
The null hypothesis, H₀, represents the reference claim against which the data are assessed. The alternative hypothesis, Hₐ, represents the direction or kind of difference the research question is asking about. In the Penn State STAT 200 presentation, hypotheses are expressed in terms of population parameters and the null contains equality: Penn State STAT 200: Normal Distributions.
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Choose the alternative to match the question before examining the results. An alternative may ask whether a parameter differs in either direction, is greater, or is less. The choice affects which outcomes count as evidence against H₀.
3. Check the design and test conditions
Choose a test that fits the study design and verify its assumptions before interpreting the data. Depending on the test, conditions may include independent observations or an appropriate sampling-distribution condition. If the conditions are not met, the test statistic and its reference distribution may not support the intended conclusion.
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- This guide is a perfect overview for the topics covered in introductory statistics courses.
Planning also means considering the consequences of errors. A Type I error is rejecting a true H₀; a Type II error is failing to reject a false H₀. These risks matter when designing a study, not just after a result appears. Penn State’s STAT 500 hypothesis-testing lesson describes the assumptions and procedural choices involved.
4. Choose α before analyzing the result
The significance level, α, is the decision threshold selected for the test and is associated with the probability of a Type I error under the procedure. A value of 0.05 is a common choice in the Penn State STAT 500 lesson, but it is not mandatory for every study; the threshold should be selected to suit the context and consequences of error.
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Choosing α in advance helps prevent changing the standard after seeing whether the data look favorable. It is a rule for making a decision, not the probability that a particular hypothesis is true.
5. Calculate the test statistic
Apply the selected test to the sample data. The test statistic summarizes how far the observed result lies from what would be expected if H₀ were true. Its formula and reference distribution depend on the parameter, test and assumptions, so there is no single statistic used for every hypothesis test.
6. Use a p-value or a rejection region
The p-value is calculated assuming H₀ is true: it is the probability of obtaining the observed test statistic, or one more extreme in the direction specified by Hₐ. It is not the probability that H₀ itself is true. Penn State’s STAT 200 lesson and STAT 100 lesson explain the introductory p-value approach.
With the p-value approach, compare the p-value with α using the test’s decision rule. Alternatively, use a critical value or rejection region established by the test and α, and check whether the statistic falls in that region. These are two ways to apply a decision rule; use the one specified for the analysis.
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7. Make the statistical decision, then explain it
If the decision rule is met, reject H₀. Otherwise, say “fail to reject H₀.” Failing to reject does not prove H₀, and rejecting H₀ does not prove Hₐ; the result is evidence assessed under the chosen model. Penn State’s STAT 500 lesson lays out the decision and conclusion stages.
Finish by translating the decision back into the original population question. Distinguish statistical significance from practical importance: a statistically significant result alone does not establish that an effect is large or consequential.
Why some guides count fewer steps
Hypothesis testing does not have one universally accepted step count. Penn State STAT 100 presents four basic steps, STAT 200 uses a five-step procedure, STAT 500 separates the process into six steps, and Penn State’s broader review groups the logic into three stages: STAT 100, STAT 200, STAT 500 and Statistical Concepts and Reasoning. These counts differ because lessons combine or separate activities such as checking assumptions, choosing α, calculating a statistic and explaining the conclusion. The underlying logic is the same: define a claim, assess data against a null model, and interpret the resulting evidence.
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