Biserial Estimators in the Presence of Guessing

Abstract

As estimators of correlation of a criterion variable with the continuous latent variable that underlies a dichotomous test item score, both the biserial correlation coefficient, r_b, and Brogden’s coefficient of selective efficiency, S^*, are severely depressed (negatively biased) by guessing, regardless of sample size or true latent correlation. Formulas and charts are given for computing better estimates, r̂ and Ŝ^*, free of guessing bias, based on observed proportions of right, wrong, and omitted answers. In Monte Carlo studies both r̂ and Ŝ^* had smaller mean square errors in the presence of guessing than r_b and S^*, and Ŝ^* stayed on target even when the latent and criterion variable were given (the same) rectangular, bimodal, or chi square distribution.