Write notes on Heterogeneity test.
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Measuring the inconsistency of studies’ results
The classical measure of heterogeneity is Cochran’s Q, which is calculated as the weighted sum of squared differences between individual study effects and the pooled effect across studies, with the weights being those used in the pooling method. Q is distributed as a chi-square statistic with k (numer of studies) minus 1 degrees of freedom. Q has low power as a comprehensive test of heterogeneity (Gavaghan et al, 2000), especially when the number of studies is small, i.e. most meta-analyses. Conversely, Q has too much power as a test of heterogeneity if the number of studies is large (Higgins et al. 2003): Q is included in each StatsDirect meta-analysis function because it forms part of the DerSimonian-Laird random effects pooling method DerSimonian and Laird 1985). An additional test, due to Breslow and Day (1980), is provided with the odds ratio meta-analysis. It is arguably not possible to examine the null hypothesis that all studies are evaluating the same effect, by considering the only the summary data from the studies: The heterogeneity test results should be considered alongside a qualitative assessment of the combinability of studies in a systematic review.
The I² statistic describes the percentage of variation across studies that is due to heterogeneity rather than chance (Higgins and Thompson, 2002; Higgins et al., 2003). I² = 100% x (Q-df)/Q. I² is an intuitive and simple expression of the inconsistency of studies’ results. Unlike Q it does not inherently depend upon the number of studies considered. A confidence interval for I² is constructed using either i) the iterative non-central chi-squared distribution method of Hedges and Piggott (2001); or ii) the test-based method of Higgins and Thompson (2002). The non-central chi-square method is currently the method of choice (Higgins, personal communication, 2006) – it is computed if the 'exact' option is selected.
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In statistics, study heterogeneity is a problem that can arise when attempting to undertake a meta-analysis. Ideally, the studies whose results are being combined in the meta-analysis should all be undertaken in the same way and to the same experimental protocols: study heterogeneity is a term used to indicate that this ideal is not fully met.