The goals and strategies of robust methods

The general theme of this paper is that we have the technology to vastly improve psychological research in any situation where ANOVA, regression, and correlation are used. Modern methods, which include robust methods as a special case, are important to applied researchers because they substantially increase our chances of detecting true differences between groups and true associations between variables, and they provide a more revealing description of how groups differ and how variables are related. Put another way, if the goal is to collect data and avoid discovering differences between groups and associations between variables, use standard methods and avoid robust techniques. Standard methods work well when conventional assumptions are true, but under arbitrarily small departures from normality, their power can be relatively poor and confidence intervals can have probability coverage that differs substantially from the nominal level. However, misconceptions about the goals and strategies of robust methods are common, perhaps because typical descriptions about them are written at a rather technical level, or because the methods are not intuitive. Consequently, one goal in this paper is to provide a relatively non‐technical summary of the foundations of robust methods and hopefully to correct many of the misconceptions that arise. Another goal is to illustrate the advantages of robust methods by re‐analysing data from various studies and demonstrating that they can lead to substantially different conclusions versus standard techniques. Yet another goal is to supplement recent reviews of robust methods by describing some recent advances.