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A Program for Estimating the Relative Efficiency of Tests at Various Ability Levels, for Equating True Scores, and for Predicting Bivariable Distributions of Observed Scores

Lees, Diana M.; Lennon, Virginia; Lord, Frederic M.; Stocking, Martha; Wingersky, Marilyn S.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
National Science Foundation (NSF), Office of Naval Research, BIV20, Equated Scores, Statistical Analysis, Test Validity, True Scores


For two tests measuring the same trait, the program, BIV20, equates the scores using the two True score distributions estimated by the univariate method 20 program (see Wingersky, Lees, Lennon, and Lord, 1969) and with these equated true scores and their distributions, estimates the bivariate distribution scores and the relative efficiency of the two tests at various ability levels. The method is described and formulas given in the appendix. If desired, this estimated distribution is compared to an actual bivariate observed score distribution provided by the user, and a chi-square between the estimated and actual distributions is computed. The program is written in Fortran IV for the IBM 360/65. Its only restriction is that the maximum number of items for each test is 50.

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