An investigation of the sampling distributions of item discrimination indices

The sampling properties of four item discrimination indices (biserialr, Cook's indexB, theU–L 27 per cent index, and DeltaP) were investigated in order to ascertain their sampling properties when small samples drawn from actual test data rather than constructed data were employed. The empirical results indicated that the mean index values approximated the population values and that values of the standard deviations computed from large sample formulas were good approximations to the standard deviations of the observed distributions based on samples of size 120 or less. Goodness of fit tests comparing the observed distributions with the corresponding distribution of the product-moment correlation coefficient based upon a bivariate normal population indicated that this correlational model was inappropriate for the data. The lack of adequate mathematical models for the sampling distributions of item discrimination indices suggests that one should avoid indices whose only real reason for existence was the simplification of computational procedures.This research reported herein was performed pursuant to a contract (OE-2-10-071) with the United States Office of Education, Department of Health, Education and Welfare.