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Common language effect size (CLES : https://en.wikipedia.org/wiki/Effect_size#Common_language_effect_size) is calculated as proportion of all possible pairs of 2 group values which are more for one group than the other. But if 2 groups are paired, then it does not make sense to have all possible pairs of values of 2 groups. How is CLES calculated for paired data? Or is it not possible to use CLES for paired data and one can only report paired t-test for these?

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For paired data, I would say to use only the pairs that you have, not all possible pairs. That makes logical sense.

Kerby (2014) (from the Wikipedia reference) says

McGraw and Wong (1992) discussed using the proportion of favorable pairs as a measure of effect size, which they called the common language effect size.

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  • $\begingroup$ How can we calculate confidence limits of CLES with paired data? $\endgroup$
    – rnso
    Apr 23, 2015 at 0:29
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    $\begingroup$ @rnso To get confidence limits, I suggest using binomial confidence intervals. To loosely explain this, if Group A wins Group B 55% of the time, in n occurrences (pairs), what is the distribution p (winning probability)? There are different variations of this, but I generally use and recommend Wilson binomial confidence interval. $\endgroup$
    – won782
    Jun 15, 2017 at 18:03

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