Introduction
This topic covers the distribution-free (non-parametric) tests used when the assumptions of parametric tests are not met, the main rank tests that replace them, and two tests for categorical data: Pearson's chi-squared test and Fisher's exact test. The key exam skill is choosing a correct test from the type of data, the study design, the number of groups and the sample size, and then interpreting the p-value correctly.
Non-parametric tests: when and why
Non-parametric tests make no assumption about the shape of the population distribution, such as normality, and do not estimate parameters like the mean or variance. They are used when data are ordinal, when the distribution is clearly skewed or has extreme outliers, or when the sample is too small to check normality. The cost is lower power when the parametric assumptions really hold, and the test answers a question about distributions or medians rather than about means.
- Parametric assumptions that may fail: normal distribution, equal variances, interval or ratio measurement, adequate sample size.
- Typical situations: scores or ranks, heavily skewed laboratory values, very small samples, data with extreme outliers.