Nonparametric Tests: When and Which

Nonparametric tests make fewer assumptions about the underlying distribution — particularly, they do not require normality. They are the right choice when data is ordinal, severely non-normal, or sample sizes are too small to verify normality.

Nonparametric vs parametric counterparts

Parametric test	Nonparametric alternative	What it tests
One-sample t-test	Sign test / Wilcoxon signed-rank	Median vs hypothesized value
Paired t-test	Wilcoxon signed-rank test	Paired differences (median)
Two-sample t-test	Mann-Whitney U (Wilcoxon rank-sum)	Difference in location between two groups
One-way ANOVA	Kruskal-Wallis test	Location differences across k groups
Pearson correlation	Spearman rank correlation	Monotonic association

How rank-based tests work

Most nonparametric tests replace raw values with their ranks (1 = smallest). The test statistic is computed from ranks, not raw values. This makes the test insensitive to outliers and non-normality.

CQE exam tips

Kruskal-Wallis is the nonparametric version of one-way ANOVA — the most tested nonparametric test on the CQE.
Nonparametric tests are less powerful than their parametric counterparts when normality holds — use parametric when assumptions are met.
Mood's median test and Kruskal-Wallis both compare multiple groups but use different statistics.

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