Alternative Approaches to Inference

Abstract

In this final chapter we consider some inferential methods that are different in important ways from those considered earlier. Recall that many of the confidence intervals and test procedures developed in Chapters 9–12 were based on some sort of a normality assumption. As long as such an assumption is at least approximately satisfied, the actual confidence and significance levels will be at least approximately equal to the “nominal” levels, those prescribed by the experimenter through the choice of particular t or F critical values. However, if there is a substantial violation of the normality assumption, the actual levels may differ considerably from the nominal levels (e.g., the use of t.025 in a confidence interval formula may actually result in a confidence level of only 88% rather than the nominal 95%). In the first three sections of this chapter, we develop distribution-free or nonparametric procedures that are valid for a wide variety of underlying distributions rather than being tied to normality. We have actually already introduced several such methods: the bootstrap intervals and permutation tests are valid without restrictive assumptions on the underlying distribution(s).