This paper considers the problem of selecting matched pairs of observations for the reduction of bias in statistical hypothesis testing. A Euclidean distance function is suggested for measuring the similarity between paired observations. The matching process is then formulated initially as an assignment problem. Alternative formulations of the problem that would reduce computational difficulty are considered. INTRODUCTONMany observational studies are designed to investigate the relationship between a continuous variable (often some measure of performance) and a dichotomous variable used to define group membership. The dichotomous variable (independent variable) is often thought to influence the continuous (dependent) variable. The frequent purpose of such studies is to investigate the consequences of alternative courses of action in order to make better decisions.Consider a commercial bank attempting to decide whether to seek membership in the Federal Reserve System. A prime consideration in the decision might be the effect of membership (the dichotomous variable) upon bank profitability (the continuous variable). A possible decision rule would be to select the alternative (membership or non-membership) that is expected to result in higher profitability. A prerequisite to an informed decision would be to investigate the relationship between membership and profitability, perhaps by contrasting the average profitability of member banks with non-member banks.'Other studies of this type include the following examples: a study to determine whether the viewing of a television broadcast affects viewer attitudes [2], a comparison of certain characteristics between financially sound and problem firms [I41 (151, and a study to determine the effect of a specific personnel program on worker turnover.A complicating factor often encountered in this type of study is the presence of additional variables, called covariables or concomitant variables (e.g., bank size and age in our first example), that are not of direct interest in the study but 'Studies of the relationship between membership in the Federal Reserve System and bank profitability have been undertaken by Gilbert and Peterson [7] and Sinkey and Walker [lS]. 62
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