# Effect size of Cochran's Q

I have performed a Cochran's Q test for a within-subjects experimental design with 3 conditions and 36 participants with a dichotomous dependent variable.

I found a (just) statistically significant effect ($\chi^2$ = 6.00, df = 2, p = 0.04979) and would like to also report the effect size, but haven't been able to find any information as to which effect measure to use and how to calculate it.

Any pointers would be gratefully received - the domain is human factors (psychology).

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## 1 Answer

I found this paper with Google but I cannot access it, so I don't really know what it is about really:

Berry KJ, Johnston JE, Mielke PW Jr. An alternative measure of effect size for Cochran's Q test for related proportions. Percept Mot Skills. 2007 Jun;104(3 Pt 2):1236-42.

I initially thought that using pairwise multiple comparisons with Cochran or McNemar test* (if the overall test is significant) would give you further indication of where the differences lie, while reporting simple difference for your binary outcome would help asserting the magnitude of the observed difference.

* I found an online tutorial with R.

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Yes, I saw that paper too, but couldn't access it :( In the end I did use McNemar's test to do pairwise tests, for which I reported effect sizes, however for the original Cochran's Q test, I never did find a suitable effect size measure. I think it is convention to report effect sizes, both for the original test and for the post-hoc pairwise tests, right? –  Ham May 25 '11 at 8:36
@Ham Yes, reporting ESs is recommended in many settings (I can think of the APA guidelines for example), although I would say reporting group difference (unstandardized, because ES are just standardized difference) is already good practice. –  chl May 25 '11 at 8:53
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