| One-Sample t-Test | Compare sample mean to a known value | Normality of the sample distribution | Wilcoxon Signed-Rank Test | Compare median of a sample to a known value | Distribution-free; does not assume normality |
| Independent t-Test | Compare means between two independent groups | Normality, equal variances in groups | Mann-Whitney U Test | Compare distributions between two independent groups | Distribution-free; does not assume normality or equal variances |
| Paired t-Test | Compare means between two related groups | Normality of the difference scores | Wilcoxon Signed-Rank Test | Compare the median of paired differences | Distribution-free; does not assume normality |
| Two-Sample t-Test | Compare means between two independent groups | Normality, equal variances in groups | Mann-Whitney U Test | Compare distributions between two independent groups | Distribution-free; does not assume normality or equal variances |
| One-Way ANOVA | Compare means across three or more groups | Normality, equal variances among groups | Kruskal-Wallis Test | Compare distributions across three or more independent groups | Distribution-free; does not assume normality or equal variances |
| Repeated Measures ANOVA | Compare means across multiple related groups | Normality, sphericity (equal variances of differences) | Friedman Test | Compare distributions across multiple related groups | Distribution-free; does not assume normality |
| ANCOVA | | | | | |