LI, B., and HUANG, X., 2009. Dichotomous transformations for statistical inference about odds ratios. Journal of Nonparametric Statistics, 21 (1), pp. 41-48
Dichotomous transformations for continuous outcomes are commonly used. In this paper, we investigate dichotomisation for statistical inference about odds ratios in a situation where two underlying distributions from which independent samples are drawn are skewed and unknown. Under some mild conditions it is shown that a suitable choice of the cutpoint of a dichotomous transformation must lie within the range bounded by the two medians of the two underlying distributions, within which there exists a unique optimal cutpoint in terms of the asymptotic efficiency of point estimation and hypothesis testing. The issue of selecting a cutpoint is also linked to the choice amongst some existing non-parametric tests.