The Cost of Dichotomization

Abstract

Assuming bivariate normality with correlation r, dichotomizing
\none variable at the mean results in the reduction
\nin variance accounted for to .647r²; and dichotomizing
\nboth at the mean, to .405r². These losses, in
\nturn, result in reduction in statistical power equivalent
\nto discarding 38% and 60% of the cases under representative
\nconditions. As dichotomization departs from
\nthe mean, the costs in variance accounted for and in
\npower are even larger. Consequences of this practice
\nin measurement applications are considered. These
\nlosses may not be quite so large in real data, but since
\nmethods are available for making use of all the original
\nscaling information, there is no reason to sustain
\nthem.