Non Parametric Statistics

Parametric methods assume that data follows a known distribution — usually the normal. Non-parametric methods make no such assumption. This poster summarises the main distribution-free tests and when to use them.

Why Non-Parametric?

• Small sample sizes where normality cannot be verified
• Ordinal or ranked data
• Presence of outliers that would distort parametric tests
• Data that clearly violates normality assumptions

One-Sample Tests

• Sign test — tests the median against a hypothesised value
• Wilcoxon signed-rank test — more powerful alternative to the sign test

Two-Sample Tests

• Mann–Whitney U test — compares two independent groups
• Wilcoxon signed-rank test — compares two related (paired) samples

K-Sample Tests

• Kruskal–Wallis test — non-parametric analogue of one-way ANOVA
• Friedman test — non-parametric analogue of repeated-measures ANOVA

Association & Correlation

• Spearman’s ρ — rank-based correlation coefficient
• Kendall’s τ — concordance-based correlation

Goodness-of-Fit

• Kolmogorov–Smirnov test — compares a sample to a reference distribution
• Chi-squared goodness-of-fit — for categorical data