0000000000199046
AUTHOR
Michael B. Dollinger
On the moments of Cochran's Q statistic under the null hypothesis, with application to the meta-analysis of risk difference.
W. G. Cochran's Q statistic was introduced in 1937 to test for equality of means under heteroscedasticity. Today, the use of Q is widespread in tests for homogeneity of effects in meta-analysis, but often these effects (such as risk differences and odds ratios) are not normally distributed. It is common to assume that Q follows a chi-square distribution, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. In this paper, the effect and weight for an individual study may depend on two parameters: the effect and a nuisance parameter. We present expansions for the first two moments of Q without any normality assumptions. Our expansions w…
Testing for homogeneity in meta-analysis I. The one-parameter case: standardized mean difference.
Meta-analysis seeks to combine the results of several experiments in order to improve the accuracy of decisions. It is common to use a test for homogeneity to determine if the results of the several experiments are sufficiently similar to warrant their combination into an overall result. Cochran's Q statistic is frequently used for this homogeneity test. It is often assumed that Q follows a chi-square distribution under the null hypothesis of homogeneity, but it has long been known that this asymptotic distribution for Q is not accurate for moderate sample sizes. Here, we present an expansion for the mean of Q under the null hypothesis that is valid when the effect and the weight for each s…