ANCOVA based on comparing a robust measure of location at empirically determined design points

Abstract

For two independent groups, let (Yij), Xij), i = 1, …, nj; J = 1, 2 be a random sample of nj observations from the jth group. Suppose that for the jth group, the population trimmed mean of Y, given that X = x, is given by some unknown function mj(x). The paper describes a method of comparing the two regression lines at q design points determined empirically. The proposed procedure is based in part on a simple application of the running interval smoother which allows mj(x) to be modelled non‐parametrically. In contrast to extant methods, it is not assumed that the error term associated with the jth group has constant variance, nor is it assumed that the variance of Y, given X, is the same for both groups. The power of the new method compares well to the conventional method when the standard assumptions of normality, parallel regression lines, and homogeneity of variance are true. The new method can have substantially higher power when standard assumptions are violated, it provides good control over the probability of a Type I error for a much wider range of situations, and it provides a more detailed indication of where regression lines differ and by how much.