Mann-Whitney U Test
Count cross-sample wins and ties, then compare U with every indexed allocation of two small samples.
Free theory articleCount cross-sample wins and ties, then compare U with every indexed allocation of two small samples.
Concept & interpretation
The Mann-Whitney U Test (also known as the Wilcoxon rank-sum test) is a non-parametric statistical test used to compare two independent samples. The exact allocation model used here assumes an exchangeable equal-distribution null: the six indexed observations can be assigned to the two independent groups with equal probability. The weaker condition that wins and losses are equally likely alone does not justify this permutation calibration. Unlike the t-test, it does not assume that the data follows a normal distribution.
Experiment
In the interactive module, you can explore the Mann-Whitney U test with two small samples of size 3.
- First, choose an option from the Sample preset select control, such as
Separated,Interlaced, orPartial ties, to set the dataset configurations. - Observe the generated 3x3 comparison grid counting wins and ties for every pair (a in A, b in B). Watch the exact 20-allocation distribution of the U statistic render as a graph, highlighting the extremeness of the observed value compared to the null distribution. Note that the equivalent average-rank sum is computationally identical to the U test without replacing tied permutation weights by distinct-value counts.