Austere Realism and the Worldly Assumptions of Inferential Statistics

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 this paper I will consider the role of one statistical concept (statistical power) and two statistical principles or assumptions (homogeneity of variance and the independence of random error), in the reliable application of selected statistical methods. I defend a tacit but widely-deployed naturalistic principle of explanation (E): Philosophers should not treat as inexplicable or basic those correlational facts that scientists themselves do not treat as irreducible. In light of (E), I contend that the conformity of epistemically reliable statistical tests to these concepts and assumptions entails at least the following modest or austere realist commitment: (C) The populations under study have a stable theoretical or unobserved structure that metaphysically grounds the observed values; the objects therefore have a fixed value independent of our efforts to measure them. (C) provides the best explanation for the correlation between the joint use of statistical assumptions and statistical tests, on the one hand, and methodological success on the other.