Non-Parametric Tests and Experimental Design

Parametric tests (t-tests, ANOVA) assume data follows a specific distribution (usually normal) and that variances are approximately equal. When these assumptions are violated — especially with small samples, highly skewed data, ordinal data, or data with extreme outliers — non-parametric tests are safer choices. Non-parametric tests work by ranking the data rather than using raw values, making them robust to non-normality. The Mann-Whitney U test (Wilcoxon rank-sum test) is the non-parametric alternative to the independent two-sample t-test. It tests whether one group's values tend to be larger than the other's by ranking all observations from both groups together and comparing rank sums. Kruskal-Wallis test is the non-parametric alternative to one-way ANOVA — comparing medians across three or more groups using ranks. Spearman rank correlation (ρ or rs) is the non-parametric alternative to Pearson correlation — it measures the monotonic relationship between two ranked variables. Spearman is appropriate when data is ordinal (e.g., satisfaction ratings 1–5), when the relationship is monotonic but not linear, or when outliers make Pearson unreliable. Spearman ρ = 1 − (6Σdᵢ²) / (n(n²−1)), where dᵢ is the difference in ranks for each pair.