Cliff's Delta (Effect Size)
Computes Cliff's delta, a non-parametric effect-size measure between two groups. It answers a direct question: if I draw a value at random from each group, how much more likely is one to be larger than the other? It ranges from −1 to +1; zero means complete overlap. Because it works only with order comparisons, it requires no assumptions about the distribution and is robust to outliers. It's the ideal companion to the Mann-Whitney test. Enter the two groups of values.
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Cliff's Delta (Effect Size)
Computes Cliff's delta, a non-parametric effect-size measure between two groups. It answers a direct question: if I draw a value at random from each group, how much more likely is one to be larger than the other? It ranges from −1 to +1; zero means complete overlap. Because it works only with order comparisons, it requires no assumptions about the distribution and is robust to outliers. It's the ideal companion to the Mann-Whitney test. Enter the two groups of values.
How separated two groups are, without means
Comparing two groups by their difference in means assumes the mean is a good summary and that the data behave. When that's not the case, with skewed or ordinal distributions, Cliff's delta offers an effect-size measure that depends on none of those assumptions, based only on order comparisons.
The definition is intuitive. Taking all possible pairs with one value from each group, you count in how many the first group is larger and in how many it's smaller. The delta is the difference between those two frequencies, divided by the total number of pairs. The result ranges from minus one, when the second group completely dominates, to plus one, when the first dominates; zero means total overlap between the groups.
Enter the two groups of values. The tool returns Cliff's delta. Because it summarizes one group's dominance over the other with no distributional assumption, it's the ideal companion for reporting the effect size of a Mann-Whitney test, translating a significant p-value into a concrete measure of how large the difference is.
Related Tools
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Computes the Mann-Whitney U test, the non-parametric alternative to the t-test for comparing two independent groups. Instead of comparing means, it compares the ranks of the combined data, which makes it valid even when the data don't follow a normal distribution or are ordinal. The tool computes the U statistic and the normal approximation z, with a tie correction. Enter the two groups of observations, separated by commas.
Mann-Kendall Trend Test
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Friedman Test
Computes the Friedman test, the non-parametric version of repeated-measures ANOVA. It's used when the same subjects (or blocks) go through three or more conditions and you want to know whether the conditions differ, without assuming normality. Within each block, the treatments are ranked; if one treatment is consistently better, it accumulates low ranks across all blocks, and the Friedman chi-square statistic grows. Enter the blocks: treatments separated by commas, blocks by semicolons.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.