How to choose the test
Three questions decide it. Is the study looking for a difference or a correlation? For a difference, are the conditions related (repeated measures or matched pairs) or independent groups? And are the data nominal (counts in categories), ordinal (ratings and ranks) or interval (equal units such as seconds or words recalled)?
| Data | Related design | Independent groups | Correlation |
|---|---|---|---|
| Nominal | Sign test | Chi-square | Chi-square |
| Ordinal | Wilcoxon | Mann-Whitney | Spearman’s rho |
| Interval | Related t-test | Unrelated t-test | Pearson’s r |
The bottom row (parametric tests) also needs data that are roughly normal, with a similar spread in each condition. OCR names only the five non-parametric tests, so for OCR interval data use the test in the ordinal row.
Finding the critical value
Find the row first: N for the sign test, Wilcoxon and Spearman’s rho (in the sign test and Wilcoxon, leave out anyone with no difference); N1 and N2 for Mann-Whitney; degrees of freedom for the rest: N − 1 for the related t-test, N1 + N2 − 2 for the unrelated t-test, N − 2 for Pearson’s r and (rows − 1) × (columns − 1) for chi-square. Then take the column for one- or two-tailed at your level. S, T and U are significant when equal to or less than the critical value; the others when equal to or more than it. A memory aid: tests with an R in the name (Spearman, Pearson, related and unrelated t, chi-square) need the calculated value to be gReater.
A worked sign test
In set P7C7A2 (AQA), 15 participants did a breathing exercise: 12 felt calmer, 2 less calm and 1 no different. Leave out the 1 with no difference, so N = 14, and S is the count of the less frequent answer: S = 2. The psychologist predicted “calmer”, so the test is one-tailed, and at p ≤ 0.05 with N = 14 the critical value is 3. S = 2 is equal to or less than 3, so the result is significant: reject the null hypothesis. Open set P7C7A2
What each course choice covers
AQA asks you to choose among all eight tests but to calculate only the sign test, so AQA sets open with a sign test and give you the calculated value for the others. Pick “Every test” under Calculate to work them all. OCR names five tests (sign, Wilcoxon, Mann-Whitney, Spearman’s rho and chi-square), and its sets calculate all five. “All 8 tests” calculates everything, including the t-tests and Pearson’s r. For mean, median, standard deviation and the normal curve (AP Psychology too), see descriptive statistics practice. For chi-square in genetics, Chi-Square Practice in the list of tools at the foot of the page has its own sets.
Questions
How do you do a sign test in psychology?
Give each participant a + or − for the direction of their difference and leave out anyone with no difference. N is the number left. S is the count of the less frequent sign. Find the critical value for N, one- or two-tailed, at your level: the result is significant if S is equal to or less than it.
How do you know which statistical test to use?
Ask three things. Is it a difference or a correlation? For a difference, are the conditions related (repeated measures or matched pairs) or independent groups? Are the data nominal, ordinal or interval? The grid above gives the test for each answer. Interval data suit a t-test or Pearson’s r only if they are also roughly normal.
What is the difference between a one-tailed and a two-tailed test?
A one-tailed test goes with a directional hypothesis, which says which way the result will go, usually because earlier research suggests it. A two-tailed test goes with a non-directional hypothesis: a difference or a correlation either way. In the table, read the row of levels that matches.
When is a result significant?
Compare the calculated value with the critical value. For the sign test (S), Wilcoxon (T) and Mann-Whitney (U) the result is significant when the calculated value is equal to or less than the critical value. For Spearman’s rho, Pearson’s r, the t-tests and chi-square it must be equal to or more than it.
What are Type I and Type II errors?
A Type I error is rejecting a null hypothesis that is true: a false positive, more likely with a lenient level such as p ≤ 0.10. A Type II error is accepting a null hypothesis that is false: a false negative, more likely with a strict level such as p ≤ 0.01. So most studies use p ≤ 0.05.
Why does my textbook’s table give a different critical value?
Printed tables come from different sources, and some differ by 1 in places. Here the sign test, Wilcoxon and Mann-Whitney values are worked out exactly, and rho follows the table exam papers print. Every practice result is kept clear of the line, so any of these tables gives the same decision. In an exam, use the table on the paper.
Sources, checked 27 October 2026: AQA AS and A-level Psychology specification 7181/7182, version 1.2 (PDF), section 4.2.3; OCR A Level Psychology H567 specification, version 1.5 (PDF), section 1.3; critical values tables printed in AQA 7182/2 (November 2021), OCR H567/01 (2021 to 2025) and Pearson Edexcel 9PS0/02 (October 2020) papers.