Which statistical test should I use in psychology?
AQA A-level Psychology 7182 inferential tests
Answer the questions
| Data | Difference, unrelated | Difference, related | Relationship |
|---|---|---|---|
| Nominal | Chi-squared test | Sign test | Chi-squared (association) |
| Ordinal | Mann-Whitney U test | Wilcoxon signed-rank test | Spearman's rho |
| Interval | Unrelated t-test parametric | Related t-test parametric | Pearson's r parametric |
Questions people ask
When do you use a sign test?
When you are testing for a difference, the design is related (repeated measures or matched pairs), and the data are nominal, or are reduced to the direction of each difference: a plus, a minus or a tie.
What is the difference between Wilcoxon and Mann-Whitney?
Both test a difference with ordinal data. Wilcoxon is for a related design (the same or matched participants), Mann-Whitney for an unrelated design (independent groups).
Is S significant if it equals the critical value?
Yes. For the sign test, S must be equal to or less than the critical value to be significant. For example, with N = 12 at p ≤ 0.05 one-tailed, the critical value is 2, so S = 2 is significant.
When do you use chi-squared?
When the data are nominal (frequencies in categories) and each participant appears in only one category: an unrelated design testing a difference, or a test of association between two variables.
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How we work this out
What it does
Answer three questions to name the test among the eight AQA lists, with the reason for each step, and work out a sign test with its critical value.
The eight inferential tests named in the AQA A-level Psychology 7182 specification (section 3.2.3.3): sign test, Wilcoxon, related t-test, chi-squared, Mann-Whitney, unrelated t-test, Spearman's rho and Pearson's r, and the calculation of the sign test.
Method
- The test follows from three decisions, in the order AQA's table sets them out: whether the study looks for a difference or a relationship, whether the design is related or unrelated (for a difference), and whether the data are nominal, ordinal or interval.
- Interval data that do not meet the parametric conditions (a roughly normal distribution, and similar variances for unrelated groups) are tested at the ordinal level.
- Sign test: N is the number of pairs with a difference (ties are left out) and S is the number of the less frequent sign.
- The critical value is the largest S whose exact binomial probability, with a half chance of each sign, is at or below the significance level (halved first for a two-tailed test). This is how printed sign-test tables are made. The result is significant when S is equal to or less than the critical value.
- For a directional (one-tailed) hypothesis the pluses are the predicted direction; when the minuses outnumber them, the result cannot support the hypothesis.