distributionfree

Distributionfree refers to statistical methods and inferences that do not rely on a specific probability distribution for the data. In practice, distribution-free methods belong to nonparametric statistics and often use ranks, signs, or order statistics rather than raw measurements. This makes them more robust to departures from common parametric assumptions, such as normality, and allows analysis of ordinal data or data with heavy tails.

Common distribution-free procedures include the Wilcoxon rank-sum test (also known as Mann-Whitney U), the Wilcoxon signed-rank test, the Kruskal-Wallis test, and rank-based correlations such as Spearman's rho and Kendall's tau. Many inferences rely on the permutation or exact distribution of ranks under the null hypothesis, which can yield p-values without assuming a particular distribution. Bootstrap resampling is often described as distribution-free because it avoids strict distributional assumptions, though its accuracy depends on sample size and representativeness.

Distribution-free methods are especially useful with small samples, ordinal data, or outliers, and when the data do not meet parametric assumptions. They often sacrifice some statistical power relative to optimally specified parametric tests when the latter's assumptions hold. They also require careful handling of ties and dependent observations, and some procedures assume continuous data to obtain exact distribution-free results.