Reporting operative effect in paired t test I just want to make sure I have something clear in my head. When I calculate the effect size for a paired samples t-test after obtaining a significant result, I simply take the mean of the differences divided by the standard deviation of the differences to get an effect size d. Do I then need to take d and divide it by the square root of 1-r, where r is the correlation between pairs and r is estimated from the sample pairs? I am confused because dividing by the square root of 1-r supposedly gives me an "operative effect size" and I'm not really sure if the operative effect size is what I should be reporting in my analyses. For example, in this report I am working on, I need to know if there was an effect size of 2 SD. So when I calculate my effect size, should I be dividing by square root 1-r? I don't think so, I think I need to report the actual detected effect size and not the operative effect, but I would love a second opinion. Thanks!
 A: If you are constructing $d$ as the mean difference divided by the standard deviation of the difference scores -- rather than by the pooled standard deviation of scores in each group, as $d$ is conventionally defined! -- then that is already what I referred to (following Cohen, 1988) as the "operative effect size." So further dividing this operative effect size by $\sqrt{1-r}$ would not make sense, because that correction is already "built in" to that instantiation of $d$. 
I think @John has a good brief discussion of different ways of computing $d$ at the bottom of his answer HERE. John mentions that some people firmly believe that $d$ should always be computed using the classical, independent-groups specificaton. I am one of these people. (Cohen was also one of these people. That's why he used the separate term "operative effect size" to talk about other ways of computing $d$.) I think it is a very bad idea to give $d$ different definitions in different contexts. Aside from the important problem this creates of killing any possible comparison of $d$ sizes between experimental paradigms that tend to use different designs, this inconsistent definition of $d$ also fosters confusion about what any given person means when they speak of $d$, unless they explicitly say which $d$ they mean! I believe this latter confusion is exactly what we have experienced here.
The "operative effect size" language convention is an attempt to allow us to talk sensibly and unambiguously about these nonstandard, but still useful, definitions of $d$ (nonstandard in the sense that they deviate from Cohen's definition). In case you are wondering, I believe Cohen calls these "operative" effect sizes because they are the effect sizes that are relevant for conducting a power analysis, which is what makes them useful. But let's keep in mind that this is only one of the uses of an effect size measure.


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*Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd edition). Routledge.

