Hypothesis Testing Step by Step: The 7 Steps With a Worked Example
Reviewed by Prof. Dr. Alexander Holtermann · Updated 16 October 2026 · 6 min read
Hypothesis testing in 7 steps: state H₀ and H₁, set α, choose the test, check assumptions, compute the statistic, decide with p, report the effect size.
Key takeaways
- Every significance test follows the same logic: assume the null hypothesis is true and ask how surprising your data would be.
- The seven steps: (1) hypotheses, (2) significance level, (3) test choice, (4) assumptions, (5) test statistic, (6) p-value and decision, (7) effect size, CI and report.
- Steps 1 to 3 belong before data collection. Deciding them afterwards invites bias and inflates false positives.
- You never “accept” or “prove” the null hypothesis; you either reject it or fail to reject it.
- A test result is only complete with an effect size and an interpretation in plain language.
The logic of a significance test
Null hypothesis significance testing (NHST) works like a proof by contradiction with uncertainty. You start by assuming the opposite of what you expect: there is no effect. Then you check whether your data fit this assumption. If data like yours would be very unlikely under “no effect”, you reject that assumption and conclude that there is an effect.
The procedure is the same for the t-test, ANOVA, chi-square test or a correlation. Only the test statistic changes. The worked example below follows a paired t-test through all seven steps.
Step 1: State the null and alternative hypotheses
The null hypothesis (H₀) states that there is no effect, no difference or no relationship in the population. The alternative hypothesis (H₁) states your expectation. Hypotheses are always about population parameters (μ, ρ), not about your sample.
Decide whether H₁ is two-sided (there is a difference in either direction) or one-sided (a difference in a specified direction). One-sided hypotheses need a strong theoretical reason stated in advance.
Steps 2 and 3: Set α and choose the test
The significance level α is the risk of a Type I error you accept, typically .05. Fix it before you see the data.
Then choose the test based on the research question, the level of measurement of the outcome and the design (see the article on choosing a statistical test). Ideally, also run a power analysis now to determine the sample size.
Step 4: Check the assumptions
Every test has assumptions. For the paired t-test: metric outcome, independent pairs, approximately normal differences. Check them with plots and descriptive statistics; formal tests support the decision but should not replace judgment, especially with small samples.
Step 5: Compute the test statistic
The test statistic measures how far your data are from what H₀ predicts, in units of the expected random variation. For the paired t-test:
t = D̄ / (s_D / √n), df = n − 1
| Quantity | Calculation | Result |
|---|---|---|
| Mean difference D̄ | (4 + 4 + 2 + 6 + 2 + 5) / 6 | 3.83 |
| SD of differences s_D | √(Σ(D − D̄)² / 5) | 1.60 |
| Standard error | 1.60 / √6 | 0.65 |
| t | 3.83 / 0.65 | 5.86 |
| df | 6 − 1 | 5 |
Step 6: Find the p-value and decide
Compare the test statistic with its distribution under H₀. Either compute the p-value or compare t with the critical value. Both give the same decision.
Decision rule: if p ≤ α, reject H₀; if p > α, do not reject H₀. Note the wording: a non-significant result means the data are compatible with H₀, not that H₀ is proven.
| Approach | Result | Decision |
|---|---|---|
| p-value, one-sided | p = .001 | .001 < .05 → reject H₀ |
| p-value, two-sided | p = .002 | also significant |
| Critical value (one-sided, α = .05, df = 5) | t_crit = 2.02; observed t = 5.86 | 5.86 > 2.02 → reject H₀ |
| Critical value (two-sided) | t_crit = 2.57 | 5.86 > 2.57 → reject H₀ |
Step 7: Effect size, confidence interval and report
Significance tells you that the effect is probably not zero; it does not tell you how large it is. Add an effect size and a confidence interval, then write a result sentence in plain language plus the APA statistics.
- Effect size: d_z = D̄ / s_D = 3.83 / 1.60 = 2.39, a very large effect.
- 95% CI for the mean reduction: 3.83 ± 2.571 · 0.65 = [2.15, 5.51] points.
- Interpretation: anxiety fell by about 4 points on average; the data are compatible with a reduction between about 2 and 5.5 points.
- Limitations: no control group, so practice effects or the approaching end of the semester could explain part of the change.
Common mistakes in hypothesis testing
Most mistakes come from mixing up what a test can and cannot say.
- Formulating hypotheses about the sample (“the mean of my sample is higher”) instead of the population.
- Deciding on one-sided testing after seeing the data.
- Writing “H₀ was accepted” or “the test proves there is no difference”. Correct: “H₀ could not be rejected.”
- Interpreting p as the probability that H₀ is true.
- Omitting the effect size or interpreting significance as practical importance.
- Testing many hypotheses without correcting for multiple comparisons.
Frequently asked questions
What are the steps of hypothesis testing?
1. State H₀ and H₁. 2. Set the significance level α. 3. Choose the test. 4. Check the assumptions. 5. Compute the test statistic. 6. Determine the p-value and decide. 7. Report effect size, confidence interval and interpretation.
What is the difference between the null and the alternative hypothesis?
The null hypothesis states that there is no effect or difference in the population. The alternative hypothesis states that there is one, either in any direction (two-sided) or in a specified direction (one-sided).
Can you accept the null hypothesis?
Not in classical significance testing. A non-significant result only means you did not find enough evidence against H₀. To show that an effect is negligible, you need equivalence tests or Bayesian methods.
What is the critical value?
The value of the test statistic at which the result becomes significant at the chosen α. For a two-sided t-test with df = 5 and α = .05 it is 2.57.
Should I use a one-sided or a two-sided test?
Two-sided by default. One-sided only if you specified the direction in advance for good reasons and a result in the other direction would be irrelevant.
Sources and further reading
- Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the Behavioral Sciences (10th ed.). Cengage.
- Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth Cengage Learning.
- Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133.
Your university’s examination regulations and style guide always take precedence.
Related articles
- Writing a hypothesisA hypothesis is a testable prediction about the relationship between variables. Write a null (H₀) and an alternative hypothesis (H₁) for each test.
- p-value and significanceThe p-value is the probability of a result at least as extreme as yours if the null hypothesis were true. p < .05 is usually called significant.
- Type I and Type II errorsA Type I error is a false positive (rejecting a true null hypothesis, risk α); a Type II error is a false negative (missing a real effect, risk β).
- Choosing a statistical testYour research question, the level of measurement of your outcome, the number of groups and whether samples are paired decide which statistical test fits.
- t-testA t-test checks whether two means differ significantly: two independent groups, two paired measurements, or one mean against a fixed value.
- Effect sizeAn effect size tells you how large a difference or relationship is, independent of sample size. Cohen’s d of 0.2, 0.5 and 0.8 is small, medium, large.
