Austere Realism and the Worldly Assumptions of Inferential Statistics

Abstract

Inferential statistical tests—such as analysis of variance, t-tests, chi-square and Wilcoxin signed ranks—now constitute a principal class of methods for the testing of scientific hypotheses. In particular, inferential statistics (when properly applied) are normally understood, for better or worse, as warranting a theoretical (typically causal) inference from an observed sample to an unobserved part of the population. These methods have been applied with great effect in domains such as population genetics, mechanics, cognitive, perceptual and social psychology, economics, and sociology, and it is not often that scientists in these fields eschew causal explanation in favor of the statement of brute correlations among properties. However, the appropriateness of a particular statistical test, and the reliability of the inference from sample to population, are subject to the application of certain statistical principles and concepts.