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TOWARD AN OPTIMAL METHOD OF EQUATING SUBGROUPS COMPOSED OF DIFFERENT SUBJECTS

机译：针对不同主题组成的子方法的最优化方法

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摘要

Whenever two or more individuals are to be compared on the basis of scores obtained from different evaluators, certain differential non-equivalence errors should be removed from their scores. A rationale for understanding how these non-equivalence errors affect a set of scores is presented. Various non-equivalence errors such as "leniency," "exaggeration," "floor and ceiling," "differential treatment of extremes," and various "composition" effects such as differential emphasis of factors, reliability, and validity are included in the rationale. The confounding effect of differential spread of ability and differen¬tial average ability among subgroups is discussed.nThe problem of optimally removing non-equivalence errors involves, first, finding the best variable or composite of variables to use as a "standardization" variable against which the data from different evaluators may be equated. One method for accomplishing this goal is described and used in the dissertation, and a second method, involving the use of canonical correlation, is discussed. Once the "standardization" variable has been determined, the problem of equating data from different evaluators may be accomplished in a variety of ways. Toops' "slope and intercept" method is here demonstrated to have the capability of removing linear non-equivalence (i.e., differential "leniency" and "exaggeration"). Another method, the "pseudo variable" approach, is proposed for the removal of linear and nonlinear ("floor or ceiling" and "differential treatment of extremes") nonequivalence errors. Toops method is shown to be a special case of the "pseudo variable" approach.nData are analyzed and transmuted by both methods, and some superiority of the nonlinear solution is demonstrated. Tests of significance for determining whether transmutation equations will significantly improve (i.e., make more "error free") a set of scores are given. The transmutation equations derived from one sample (N = 61 2), seven subgroups of data, were shown to be able to remove 21.6 per cent of the non-transmuted unexplained variance. In a second sample (N=605) of data the same equations were able to remove 18.64 per cent of the unexplained variance.n|t is recommended that whenever the relative merit of two or more individuals must be determined on the basis of scores derived from different evaluators use of the methods described here be considered.

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