StatReason

Cliff's Delta Calculator

Measure how consistently values in one group exceed values in another, using every possible pairwise comparison between the two groups rather than summarizing each group with a single number first.

What this answers

This calculator answers "if I pick one random observation from Group A and one from Group B, how much more likely is A's value to be higher than lower?" a direct probability-based interpretation that many find more intuitive than a rank-sum statistic.

How it is calculated

Every possible pair, one value from Group A and one from Group B, is compared directly. Delta is the number of pairs where A exceeds B, minus the number where B exceeds A, divided by the total number of pairs compared. Delta ranges from negative 1 (every pair favors B) to positive 1 (every pair favors A), with 0 indicating no net dominance in either direction. Tied pairs count toward neither the favorable nor unfavorable total, only toward the shared denominator.

Worked example

For Group A of 1 and 2 compared against Group B of 3 and 4, every one of the 4 possible pairs favors Group B (every A value is smaller than every B value), giving a delta of exactly negative 1, the strongest possible dominance in Group B's favor.

Assumption audit

Calculated from your data: every pairwise comparison between the two groups, split into favorable, unfavorable, and tied counts, and the resulting delta.
Evidence to review: how many pairs are tied; a large share of ties (from coarse measurement or a discrete outcome scale) shrinks the effective information behind delta even when the nontied comparisons show a clear pattern.
You must verify: that your two groups are genuinely independent samples, and that "which group tends to have higher values" is the specific question you want an effect size for, rather than a difference in means.

What this result does not mean

Cliff's delta measures ordinal dominance between distributions, not a difference in means or medians, and not causation between group membership and the outcome. Common convention labels are sometimes attached to delta's magnitude (small, medium, large), but this calculator treats those labels as nonuniversal and reports only the number itself.

Limitations

This calculator does not provide a p-value; combine it with the Mann-Whitney U Test on the same two groups (which is mathematically related to Cliff's delta) if you need a formal significance test alongside this effect size.