Statistical testing and null distributions: What to do when samples are not random.

Abstract

Selected literature related to statistical testing is reviewed to compare the theoretical models underlying parametric and nonparametric inference. Specifically, we show that these models evaluate different hypotheses, are based on different concepts of probability and resultant null distributions, and support different substantive conclusions. We suggest that cognitive scientists should be aware of both models, thus providing them with a better appreciation of the implications and consequences of their choices among potential methods of analysis. This is especially true when it is recognized that most cognitive science research employs design features that do not justify parametric procedures, but that do support nonparametric methods of analysis, particularly those based on the method of permutation/randomization.