A Coefficient of Equality for Questionnaire Items With Interval Scales

Abstract

Given a sample of n responses to a pair of questionnaire items with interval scale values of V ₁, V ₂, ..., V_k it is sometimes of interest to know the degree to which respondents select the same response for both items. The coefficient of equality is designed to measure the departure from independence in the direction of equality. If the sample means and variances of the two items are equal this coefficient is equivalent to the Pearson product moment correlation coefficient. If the sample observations on the two items are such that the joint frequencies are the product of the marginals (independence) then the coefficient of equality is 0.