Every statistical test, explained.

Use this when the same people (or matched pairs) are measured twice — before vs after, or under two conditions — and you want to know whether the average change is real. It tests whether the mean of the within-pair differences is zero on a continuous outcome. Because each person is their own control, it cancels between-person variation, making it far more powerful than comparing two separate groups at the same sample size. It assumes the differences are roughly normal (Shapiro–Wilk). Reports the mean difference, 95% CI, t, p and Cohen's dz. If normality fails, StatMinds routes to the Wilcoxon signed-rank test.

Use this to compare the average of a continuous outcome between two separate, unrelated groups — treatment vs control, or men vs women. It tests whether the two population means differ. It assumes each group is roughly normal and, in its classic form, that the groups have equal variances; when they don't, StatMinds applies Welch's correction automatically. It reports the mean difference, 95% CI, t, degrees of freedom, p and Cohen's d for effect size. With small, skewed samples or clear outliers it routes to the Mann–Whitney U test. Groups must be independent — no participant may appear in both.

Use this to check whether one group's mean differs from a specific known or hypothesized value — is the average class score different from the national benchmark of 60, or does a machine fill bottles to exactly 500 ml? It tests whether your sample mean is consistent with that reference value on a continuous outcome. It assumes the data are roughly normal, or the sample is large enough for the mean to be stable. It reports the sample mean, the difference from the reference, 95% CI, t, p and Cohen's d. If normality is doubtful, use the Wilcoxon signed-rank test.