Simplified formulas for item selection and construction

The formula for the Pearson correlation coefficient of a dichotomous variable with a multiple-categoried variable is simplified for computational purposes by effecting in the multiple-categoried variable two types of arbitrary distributions: (1) rectangular and (2) proportional to binomial expansion coefficients. The formulas which result are convenient for the selection of test items and are applicable to the objective estimation of the comparative merits of the alternatives in multiple-choice test items. It is shown that the authoritative answer should have a high positive criterion coefficient, while the omissions and several wrong-answer alternatives should each have low (algebraic) negative criterion coefficients.