The Use of the Rank Transform in Regression

Abstract

The rank transform is a simple procedure which involves replacing the data with their corresponding ranks. The rank transform has previously been shown by the authors to be useful in hypothesis testing with respect to experimental designs. This study shows the results of using the rank transform in regression. Two sets of data given by Daniel and Wood [8] are considered for purposes of illustrating the rank transform in simple and multiple regression. Also given are the results of a Monte Carlo study which compares regression on ranks with some published Monte Carlo results on isotonic regression. This Monte Carlo study is also modified to compare regression on ranks with robust regression. Another illustration gives the results of analyses on large computer codes by regression on ranks. The rank transform is a simple, repeatable process that compares favorably with other methods such as given by Andrews [1]. Our studies indicate the method works quite well on monotonic data.