Combining Data from “Related” Experiments

Abstract

It is not uncommon that the experimental data that is available in a particular statistical investigation is accompanied by collateral information drawn from other sources. The possibility of exploiting auxiliary information, be it empirical or subjective, in order to improve one’s inferences is a challenge that has intrigued statisticians for decades. Indeed, the fields of Bayesian statistics, empirical Bayes inference and meta-analysis each focus on particular prescriptions for appropriately combining information from disparate sources, and each can be thought of as a way of exploiting information auxiliary to the experiment of current interest. Excellent overviews of these varied approaches to combining information include Gaver et al. (1992), a treatise which covers general approaches, and the monographs by Hedges and Olkin (1985) on meta-analytic techniques and by Maritz and Lwin (1989) on empirical Bayes methods. Notable contributors to this literature include Fisher (1932), Cochran (1937), Savage (1954), Robbins (1956), Glass (1978) and Deely and Lindley (1981).