Modern Robust Statistical Methods: Basics with Illustrations Using Psychobiological Data

Abstract

Psychological studies in general, and psychobiological studies in particular, routinely use a collection of classic statistical techniques aimed at comparing groups or studying associations. A fundamental issue is whether violating the basic assumptions underlying these methods, namely normality and homoscedasticity, can result in relatively poor power or miss important features of the data that have practical significance. In the statistics literature, hundreds of papers make it clear that under general conditions the answer is yes and that routinely used strategies for dealing with violations of assumptions can be unsatisfactory. Moreover, a vast array of new and improved techniques is now available for dealing with violations of assumptions, including more flexible methods for dealing with curvature. The paper reviews the major insights regarding standard methods, explains why some seemingly reasonable methods for dealing with violations of assumptions are technically unsound, and then outlines methods that are technically correct. It then illustrates the practical importance of modern methods using data from the Well Elderly II study.