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Non Parametric Statistics
A course to study our non-ideal (non-normally distributed) world!
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