A combination of tests and publication bias in meta-analysis

The existing methodology for meta-analysis is reviewed and some improvements are suggested. A study is made of "Combination of tests" where an overall test-statistic is to be produced having particular optimal properties. Most of the existing statistics do not have all the optimal properties. A new statistic is proposed which has the desired properties of admissibility, Bahadur optimality and higher power than Fisher's statistic which is the only one having the first two properties.; A large sample test for checking homogeneity is available in the literature. The sampling distribution of the same statistic for small samples is studied and the critical values are tabulated.; Next, publication bias resulting from non-publication of some studies not yielding significant results, is considered. Several ways of detecting publication bias and adjusting for it in statistical inference are discussed. A new method is proposed for estimating the number of unpublished studies. The competing explanation of the variability in the data due to heterogeneity and publication bias is illustrated through an example.