# Testing for Homogeneity in Meta-Analysis I. The One Parameter Case: Standardized Mean Difference - Statistics > Methodology

Testing for Homogeneity in Meta-Analysis I. The One Parameter Case: Standardized Mean Difference - Statistics > Methodology - Download this document for free, or read online. Document in PDF available to download.

Abstract: Meta-analysis seeks to combine the results of several experiments in order toimprove the accuracy of decisions. It is common to use a test for homogeneityto determine if the results of the several experiments are sufficiently similarto warrant their combination into an overall result. Cochran-s Q statistic isfrequently used for this homogeneity test. It is often assumed that Q follows achi-square distribution under the null hypothesis of homogeneity, but it haslong been known that this asymptotic distribution for Q is not accurate formoderate sample sizes. Here we present formulas for the mean and variance of Qunder the null hypothesis which represent O1-n corrections to thecorresponding chi-square moments in the one parameter case. The formulas arefairly complicated, and so we provide a program available atthis http URL for makingthe necessary calculations. We apply the results to the standardized meandifference Cohen-s d-statistic and consider two approximations: a gammadistribution with estimated shape and scale parameters and the chi-squaredistribution with fractional degrees of freedom equal to the estimated mean ofQ. We recommend the latter distribution as an approximate distribution for Q touse for testing the null hypothesis.

Author: ** Elena Kulinskaya, Michael B. Dollinger, Kirsten Bjørkestøl**

Source: https://arxiv.org/