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Which statistical test should I use?
Answer three questions. You get the test, the reason, and a calculator or table to run it.
The full decision table
| Question | 1 sample | 2 samples | 3+ samples |
|---|---|---|---|
| Means, normal | One-sample t | Two-sample t (Welch) · paired t | One-way ANOVA |
| Medians, non-normal | Wilcoxon signed-rank / sign | Mann-Whitney · Wilcoxon (paired) | Kruskal-Wallis |
| Proportions | One-proportion z / exact binomial | Two-proportion z / Fisher exact | Chi-square (contingency table) |
| Variances | Chi-square for variance | F-test · Levene | Bartlett · Levene |
Read more: Which hypothesis test to use (guide) · Nonparametric tests · p-value explained · Type I vs Type II error
FAQ
Why does normality change the test?
t-tests, ANOVA and the F-test assume roughly normal data. With large samples they tolerate moderate skew, but small skewed samples call for a nonparametric test, which compares medians or ranks instead.
What makes data paired?
Each value in one group belongs with one value in the other: the same part before and after, or the same sample on two gages. Pairing removes part-to-part variation, so treat paired data as pairs.
Why not run many t-tests instead of ANOVA?
Each test carries its own α risk, so ten t-tests at α = 0.05 have about a 40% chance of at least one false alarm. ANOVA tests all the means at once at the stated α.
How do I check normality?
A histogram and a normality test such as Anderson-Darling. The descriptive statistics calculator does both.
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