The cost of dichotomization

Abstract

Assuming bivariate normality with correlation r, dichotomizing one variable at the mean results in the reduction in variance accounted for to .647r²; and dichotomizing both at the mean, to .405r². These losses, in turn, result in reduction in statistical power equivalent to discarding 38% and 60% of the cases under representative conditions. As dichotomization departs from the mean, the costs in variance accounted for and in power are even larger. Consequences of this practice in measurement applications are considered. These losses may not be quite so large in real data, but since methods are available for making use of all the original scaling information, there is no reason to sustain them.