Relative Distributional Methods

Relative distribution methods are a non–parametric statistical framework for analyzing data in a fully distributional context. The methods combine the graphical tools of exploratory data analysis with a framework for statistical decomposition and inference. The relative distribution is similar to a density ratio, and is based on the direct comparison of one distribution to another. It is technically defined as the random variable obtained by transforming a variable from a comparison group by the cumulative distribution function (CDF) of that variable for a reference group. This transformation produces a set of observations, the relative data, that represent the rank of the original comparison value in terms of the reference group’s CDF. The relative data preserve the information needed to compare the two original distributions. The density and CDF of the relative data can therefore be used to fully represent and analyze distributional differences. Analysis can move beyond comparisons of means and variances to fully tap the information inherent in distributions. The analytic framework is general and flexible, as the relative density is decomposable into location, shape and covariate effects.