Verteilungsfreier

Verteilungsfreier refers to a class of statistical methods that do not make assumptions about the specific probability distribution of the underlying data. These methods are also known as non-parametric tests. Unlike parametric tests, which rely on assumptions like normality or homogeneity of variances, verteilungsfreier tests are more flexible and can be applied to a wider range of data types, including ordinal and nominal data, as well as continuous data that do not meet parametric assumptions.

The advantage of verteilungsfreier methods lies in their robustness and applicability when parametric assumptions are violated. They often work by ranking the data or by examining the signs of differences between observations. Common examples of verteilungsfreier tests include the Mann-Whitney U test (an alternative to the independent samples t-test), the Wilcoxon signed-rank test (an alternative to the paired samples t-test), and the Kruskal-Wallis test (an alternative to the one-way ANOVA).

While verteilungsfreier tests offer flexibility, they can sometimes be less statistically powerful than their parametric counterparts when the assumptions of the parametric tests are met. This means that for the same sample size, a parametric test might be more likely to detect a true effect if its assumptions hold. However, when assumptions are not met, a verteilungsfreier test can be more appropriate and yield more reliable results. The choice between parametric and verteilungsfreier methods depends on the nature of the data and the research question being addressed.