Common-Language Effect Size (CLES)
Computes the common-language effect size (CLES), also called the probability of superiority. It's the most intuitive way to communicate a difference between groups: the probability that a value drawn from the first group is larger than a value drawn from the second. A CLES of 0.70 means that, in 70% of random comparisons, the first group wins. Ties count as half. It's the friendly version of Cliff's delta. Enter the two groups of values.
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Common-Language Effect Size (CLES)
Computes the common-language effect size (CLES), also called the probability of superiority. It's the most intuitive way to communicate a difference between groups: the probability that a value drawn from the first group is larger than a value drawn from the second. A CLES of 0.70 means that, in 70% of random comparisons, the first group wins. Ties count as half. It's the friendly version of Cliff's delta. Enter the two groups of values.
The difference between groups in plain language
Effect sizes like Cohen's d are useful, but unintuitive for non-statisticians. What, in practice, is a d of 0.8 worth? The common-language effect size solves this by translating the difference between two groups into a simple probability that anyone understands at once.
The idea is direct: draw a value at random from each group and ask the chance that the first group's value is the larger one. That probability is the CLES. It's computed by counting, over all possible pairs between the groups, in how many the first wins, with ties worth half a point. A CLES of 0.5 means indistinguishable groups; the closer to 1, the more the first group stands out.
Enter the two groups of values. The tool returns the probability of superiority. It's the friendliest way to communicate results: saying one treatment beats the other in 70% of comparisons is far more tangible than reporting a delta or a p-value. Mathematically, it's a direct transformation of Cliff's delta.
Related Tools
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 โ1 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.
Eta-Squared (Effect Size)
Computes eta-squared (ฮทยฒ), an effect-size measure for analysis of variance, from the F-statistic and the degrees of freedom. While the F-test says whether there's a significant difference between groups, ฮทยฒ says how much of that difference the grouping variable explains โ the proportion of total variance attributable to the groups. It's essential for reporting ANOVA results beyond the p-value. Enter the F-statistic and the numerator and denominator degrees of freedom.
Cohen's h (Effect Size for Proportions)
Computes Cohen's h, the effect-size measure for the difference between two proportions. Comparing proportions directly is misleading, because the same arithmetic difference weighs differently near the middle (0.5) and near the ends (0 or 1). Cohen's h fixes this by applying the arcsine transformation, which stabilizes the variance, before measuring the distance. Usual convention: 0.2 is small, 0.5 medium and 0.8 large. Enter the two proportions (between 0 and 1).
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.