Distributionsfria

Distributionsfria refers to statistical methods whose sampling distribution does not depend on a specific population distribution. In English, this is often called nonparametric or distribution-free statistics. Such methods typically use ranks, signs, or other order information rather than the actual data values, making them robust to outliers and suitable for ordinal data or non-normal distributions. They require fewer assumptions about the form of the underlying distribution, but may lose efficiency when the data do come from a well-specified parametric model.

Common distribution-free techniques include the sign test and the Wilcoxon signed-rank test for paired data, the Mann-Whitney U test for two independent samples, and the Kruskal-Wallis and Friedman tests for more than two groups. Correlation can be assessed with Spearman's rank correlation or Kendall's tau. Some tests are designed to be exact under the null hypothesis, and others rely on asymptotic approximations that are independent of the parent distribution.

Advantages include applicability to small samples, handling of ordinal data, and resistance to outliers, while limitations involve typically lower power than parametric counterparts when parametric assumptions hold, and complexities in interpreting effect sizes or confidence intervals.