Choosing a statistical test
Pick the test from what you are comparing and how the outcome is measured: means of scale outcomes use t tests and ANOVA, ranks of ordinal or skewed outcomes use Mann-Whitney, Wilcoxon or Kruskal-Wallis, and two categorical variables use chi-square.
| Question | Outcome | Use | Nonparametric alternative |
|---|---|---|---|
| Is one mean different from a fixed value? | Scale | One-sample t test | Wilcoxon one-sample (planned) |
| Do two separate groups differ? | Scale | Independent-samples t test | Mann-Whitney U |
| Did the same people change (before/after)? | Scale | Paired-samples t test | Wilcoxon signed-rank |
| Do three or more groups differ? | Scale | One-way ANOVA | Kruskal-Wallis H |
| Are two categorical variables related? | Nominal | Chi-square (Crosstabs) | Fisher's exact test (2×2) |
| Do two scale variables go together? | Scale | Pearson r | Spearman rho |
| Can I predict an outcome from several variables? | Scale | Linear regression | — |
| Do my questionnaire items hang together? | Items | Cronbach's alpha | — |
Check the assumptions with Explore first. If the outcome is ordinal (e.g. a single Likert item) or clearly skewed with a small sample, use the nonparametric column.