Mann-Whitney Test for Two Independent Groups

Abstract

The Mann-Whitney U test is a popular nonparametric method used to compare two independent groups when data do not meet the assumptions required for traditional parametric tests, such as normality or equal variances. Developed by Mann and Whitney in 1947, and also known as the Wilcoxon Rank-Sum test, it works by ranking all observations from both groups and examining differences in these ranks, making it suitable for ordinal data, skewed distributions, or small sample sizes. This test is widely used in fields like education, psychology, health sciences, and social research, where real-world data often deviates from ideal conditions. Its main advantage is that it reduces the impact of outliers and extreme values, but it can be sensitive to differences in distribution shapes and may be less powerful than parametric tests when the data are actually normal. Statistical software such as SPSS, R, Python, or Jamovi allows researchers to perform the test easily, automatically calculating the U statistic, handling tied ranks, and producing p-values. Interpreting results involves looking at the median ranks, p-values, and effect sizes to understand both statistical and practical significance. Compared to parametric alternatives like the independent t-test, the Mann-Whitney U test offers a flexible and reliable way to compare two independent groups, providing meaningful insights even when data are non-normal or measured on an ordinal scale.