Simulation study of Q statistic with constant weights for testing and estimation of heterogeneity of standardized mean differences in meta-analysis
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Cochran's Q statistic is routinely used for testing heterogeneity in meta-analysis. Its expected value is also used for estimation of between-study variance τ^2. Cochran's Q, or Q_IV, uses estimated inverse-variance weights which makes approximating its distribution rather complicated. As an alternative, we are investigating a new Q statistic, Q_F, whose constant weights use only the studies' effective sample sizes. For standardized mean difference as the measure of effect, we study, by simulation, approximations to distributions of Q_IV and Q_F, as the basis for tests of heterogeneity and for new point and interval estimators of the between-study variance τ^2. These include new DerSimonian-Kacker (2007)-type moment estimators based on the first moment of Q_F, and novel median-unbiased estimators of τ^2.
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