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I am performing a meta-analysis where my effects are mainly one-sample test against the chance level. Let's say that we have n subjects that perform several trials with a binary response (correct, wrong) and then I compute an accuracy index e.g. 0.7. All papers report a t-test against the chance level (e.g. 0.5) and then a cohen's d. I think that a more appropriate effect size measure could be a cohen's h or more generally a difference between two proportions, in this case one sample proportion and a population (chance) proportion. However, I'm not able to find a formula to compute the variance (for the inverse-variance weight) in this particular situation.

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