2011
DOI: 10.1002/jrsm.54
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On the moments of Cochran's Q statistic under the null hypothesis, with application to the meta‐analysis of risk difference

Abstract: 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 indi… Show more

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Cited by 42 publications
(62 citation statements)
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“…This means that the random-effects model, and so the methods used here, can be quite a crude approximation when applied to real data. Kulinskaya and colleagues [34, 35] show that the distribution of quadratic forms in meta-analysis, when applied to real data, differ from their theoretical distributions under the random-effects model. We regard this as a serious problem only when the studies are small, although this can quite often be the case in application.…”
Section: Discussionmentioning
confidence: 99%
“…This means that the random-effects model, and so the methods used here, can be quite a crude approximation when applied to real data. Kulinskaya and colleagues [34, 35] show that the distribution of quadratic forms in meta-analysis, when applied to real data, differ from their theoretical distributions under the random-effects model. We regard this as a serious problem only when the studies are small, although this can quite often be the case in application.…”
Section: Discussionmentioning
confidence: 99%
“…Third, that average value of Q has a different form for each choice of the measure of effect. Kulinskaya et al investigated the standardized mean difference and the risk difference, and Kulinskaya and Dollinger investigated the odds ratio. In all these cases, the formula for the average value involves constants that must be estimated from the data in each meta‐analysis.…”
mentioning
confidence: 99%
“…However, Kulinskaya et al . (, ) show that results concerning quadratic forms in meta‐analysis that rely on the assumptions of the random effects model can be poor approximations when applied to real datasets, and all the methods that follow are subject to these issues. Methods that take into account the fact that the within‐study variances are estimated have been proposed (Böhning et al, ; Malzahn et al, ), but at present, our methodology does not attempt this.…”
Section: The Random Effects Modelmentioning
confidence: 99%