The Expected Number of Matches and its Variance for Matched-Pair Designs

SUMMARY A mathematical model for the derivation of the expected number of matched pairs is presented, employing only that information which can be assumed at the planning stage of research. An approximate expression for calculating the sample variance is derived empirically. Using numerical values of the expected number of matches, for varying sample sizes, numbers of matching categories and matching distributions, it is shown that (a) in order to pair match all (or most) of an initial sample of cases the control reservoir has to be at least five to ten times as large in most situations; (b) for two samples of comparable size, the expected number of matches never reaches 100 per cent; and (c) when the number of categories is equivalent to the number in equal initial samples, only 50 per cent of the maximum pairs can be expected. The implications of these results for the planning of research are discussed.