The Biserial-Phi Correlation Coefficient

ABSTRACT The correlation coefficient appropriate in a fourfold situation resulting from the crossing of two dichotomous variables depends on whether the dichotomies are true or arbitrary. Almost all sources dealing with the fourfold situation discuss only the pure cases (both dichotomies true or both dichotomies arbitrary). The mixed case (one dichotomy true and the other arbitrary), introduced at least four decades ago and accompanied in more than one source with the wrong formula for the coefficient, is reintroduced in this study. In addition, a correction for unequal sample size respecting the true dichotomy is presented.