The Dominance Matrix, made visible

This is a web application to compute Cliff's delta effect size. Cliff's delta is a robust and intuitive measure of effect size that reflects the degree of difference between two groups of data. Unlike commonly used effect-size tests such as Cohen's d, Cliff's delta does not rely on the assumption of normally distributed data. This makes it especially appropriate for non-normal or ordinal data, where variance is reduced. Even when normality assumptions are met, using Cliff's delta carries no disadvantage.

The calculation of Cliff's delta involves comparing every value in one group with every value in the other group, which requires access to the raw dataset rather than summary statistics like means and standard deviations. The resulting statistic ranges from −1 to +1: values near the extremes indicate no overlap between groups, while 0 signifies complete overlap. If both the maximum and minimum variances are above or below 0, then statistical significance is observed by one of the groups (Group A > Group B). The sign of the statistic reflects which group has larger values, depending on how the groups are ordered (e.g., which one is entered as Column 1), though the absolute magnitude remains unaffected by this choice.

This page is the insight mode showing the dominance matrix and calculations of Cliff's delta and other statistics. The educational mode is to provide insight only and has a limit of 20 n-values per group. If you have your data ready and want to actually calculate Cliff's delta then click on the "Switch to Calculator Mode" button.