“The Relevance of Group Membership for Personnel Selection: A Demonstration Using Bayes’ Theorem”, 1994-09-01 (; backlinks; similar):
A Bayesian approach to problems of personnel selection implies a fundamental conflict between non-discrimination and merit selection. Groups—such as ethnic groups, sexes and races—do differ in various attributes relevant to vocational success, including intelligence and personality.
This journal has repeatedly discussed the technical and ethical issues raised by the existence of groups (races, sexes, ethnic groups) that frequently differ in abilities and other job-related characteristics (Eysenck 1991, 1992; 1990, 1991). This paper is meant to add to that discussion by providing mathematical proof that consideration of such groups is, in general, necessary in selecting the best employees or students.
It is almost an article of faith that race, sex, religion, national origin, or similar classifications (which will be referred to here as groups) are irrelevant for hiring, given a goal of selecting the best candidates. The standard wisdom is that those selecting for school admission or employment should devise an unbiased (in the statistical sense) procedure which predicts individual performance, evaluate individuals with this, and then select the highest ranked individuals. However, analysis shows that even with statistically unbiased evaluation procedures, group membership may still be relevant. If the goal is to pick the best individuals for jobs or training, membership in the group with the lower average performance (the disadvantaged group) should properly be held against the individual. In general, not considering group membership and selecting the best candidates are mutually exclusive.
…Related Psychometric Discussions: How does the conclusion reached above about the relevance of groups membership relate to discussions in the technical psychometric literature?
At least some psychometricians have been aware of the relevance of group membership. 1976 point out that differences in group means will typically lead to differences in intercepts. Jensen (198044ya, p. 94, Bias in Mental Testing) points out that the best estimate of true scores is obtained by regressing observed scores towards the mean, and that if there are 2 groups with different means, the downwards correction for the high scoring individuals will be greater for those from the low scoring group. Kelley (194777ya, p. 409, Fundamentals of Statistics) put it as follows: “This is an interesting equation in that it expresses the estimate of true ability as a weighted sum of 2 separate estimates, one based upon the individual’s observed score, X1, and the other based upon the mean of the group to which he belongs, M1. If the test is highly reliable, much weight is given to the test score and little to the group mean, and vice versa”, although he may not have been thinking of demographic groups. et al 1972 (The Dependability of Behavioral Measurements: Theory of Generalizability for Scores and Profiles) discuss the problem of deducing universe scores (essentially true scores in traditional terminology) from test data, recognizing that group means will be relevant. They even display an awareness that, since blacks normally score lower than whites, the logic of their reasoning calls for the use of higher cut-off scores for blacks than for whites (see p. 385). 1993 also displays an awareness that group means are relevant, although he feels it would be unfair to use them.
In general, the relevance of group membership has been known to the specialist psychometric community, although few outside the community are aware of the effect. Thus, the contribution of Bayes’ theorem is to provide another demonstration, one that those outside the psychometric community may be more comfortable with.