Abstract: Matched sampling is a method of data collection designed to reduce bias and variability due to specific matching variables. Although often used to control for bias in studies in which randomization is practically impossible, there is virtually no statistical literature devoted to investigating the ability of matched sampling to control bias in the common case of many matching variables. An obvious problem in studying the multivariate matching situation is the variety of sampling plans, underlying distributions, and intuitively reasonable matching methods. This article considers one class of multivariate matching methods which yield the same percent reduction in expected bias for each of the matching variables. The primary result is the derivation of the expression for the maximum attainable percent reduction in bias given fixed distributions and fixed sample sizes. An examination of trends in this maximum leads to a procedure for estimating minimum ratios of sample sizes needed to obtain well-matched samples.

INTRODUCTION

This introduction is brief; the reader is referred to Rubin [1976b] for a more detailed explanation of the notation and terminology.

Let G1 and G2 be two random samples of sizes N1 and N2 from two populations, P1 and P2. Matched sampling is an attempt to find subsamples of G1 and G2, G1* and G2* of sizes N1* and N2*, such that the distributions of the p matching variables X are more similar in G1* and G2* than in G1 and G2.