U de Mann-Whitney

The Mann-Whitney U is a statistic used in non-parametric tests to compare two independent samples. It assesses whether the two samples come from populations with the same distribution. The calculation is based on the sum of the ranks of the observations in one of the samples. The formula U = R₁ - n₁(n₁+1)/2 is used, where R₁ is the sum of the ranks of the first sample and n₁ is the size of the first sample.

This test is particularly useful when the samples do not follow a normal distribution or when the data are ordinal. It helps to determine if there is a significant difference between the medians of the two samples. The Mann-Whitney U is an alternative to the Student t-test when parametric assumptions are not met.

When interpreting the results, it is essential to consider the sample sizes and the magnitude of the U statistic. A small value of U indicates that the samples have different distributions. However, it is also crucial to evaluate the associated p-value to determine statistical significance.

A common caution when using the Mann-Whitney U is to ensure that the observations are independent and that the samples are random. Additionally, it is recommended to visually explore the data with scatter plots or histograms to get an intuitive sense of the distributions.