[Wiley Series in Probability and Statistics] Statistical Meta-Analysis with Applications || Recovery of Interblock Information

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

• Publisher: John Wiley & Sons, Inc.
• Year: 2008
• Tongue: English
• Weight: 645 KB
• Edition: 1
• Category: Article
• ISBN: 0470290897
• DOI: 10.1002/9780470386347.ch14

✦ Synopsis

In this chapter we provide a different kind of application of meta-analysis which arises in the context of analysis of data obtained from specially designed experiments.

In block designs with fixed treatment effects and no interaction, it is a well-known (and an easily verifiable) fact that the usual least-squares estimator of the treatment effects, computed assuming that the block effects are fixed, continues to provide an unbiased estimator of the treatment effects even when the block effects are random. This least-squares estimator of the treatment effects is referred to as the intrablock estimator since it is based on contrasts among the observations within the blocks, thereby eliminating the block effects. Similarly, the usual F test (known as the intrablock F test) can always be used to test the equality of the treatment effects irrespective of whether the block effects are fixed effects or random effects. However, when the block effects are random as opposed to being fixed and are independently and identically distributed as normal, additional information is available for inference concerning the treatment effects. Such information is referred to as interblock information and this information is based on the sum of the observations in each block. An important problem in this context is that of suitably combining the intrablock and interblock information to obtain a combined estimator of the treatment effects or to obtain a combined test for the equality of the treatment effects. Such a problem of Statistical Meta-Analysis with Applications.