[Wiley Series in Probability and Statistics] Statistical Meta-Analysis with Applications || Tests of Homogeneity in Meta-Analysis

✍ Scribed by Hartung, Joachim; Knapp, Guido; Sinha, Bimal K.

• Publisher: John Wiley & Sons, Inc.
• Year: 2008
• Tongue: English
• Weight: 509 KB
• Edition: 1
• Category: Article
• ISBN: 0470290897
• DOI: 10.1002/9780470386347.ch6

✦ Synopsis

As has been mentioned earlier, meta-analysis of results from different experiments or studies is quite common these days. However, as has been emphasized, it is equally important to make sure that the underlying effect sizes arising out of these experiments are indeed homogeneous before performing any meta-analysis or pooling of evidence or data so that an inference on a common effect makes sense.

In this chapter we discuss at length the problem of testing homogeneity of means in a one-way fixed effects model. We assume throughout that the observations are drawn from k independent univariate normal populations with means p1, . . . , pk and variances of, a:, . . . , a:, and the problem is to test the homogeneity hypothesis with respect to means, given by HO : p1 = . . = p k , against a general alternative. Once Ho is accepted, we feel quite comfortable in pooling all the data sets in order to make suitable inference about the common unknown mean p. The next chapter, Chapter 7, deals with the dual problem of testing homogeneity of means in a one-way random effects model, which indeed also has a long and rich history.

The problem of testing the homogeneity of means in a one-way analysis of variance (ANOVA) is one of the oldest problems in statistics with applications in many diverse fields (Cochran, 1937). Under the classical ANOVA assumption of normality, independence, and homogeneous error variances