Behavioristic, Evidentialist, and Learning Models of Statistical Testing

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Abstract
While orthodox (Neyman-Pearson) statistical tests enjoy widespread use in science, the philosophical controversy over their appropriateness for obtaining scientific knowledge remains unresolved. I shall suggest an explanation and a resolution of this controversy. The source of the controversy, I argue, is that orthodox tests are typically interpreted as rules for makingoptimal decisionsas to how tobehave–-where optimality is measured by the frequency of errors the test would commit in a long series of trials. Most philosophers of statistics, however, view the task of statistical methods as providing appropriate measures of theevidential-strengththat data affords hypotheses. Since tests appropriate for the behavioral-decision task fail to provide measures of evidential-strength, philosophers of statistics claim the use of orthodox tests in science is misleading and unjustified. What critics of orthodox tests overlook, I argue, is that the primary function of statistical tests in science is neither to decide how to behave nor to assign measures of evidential strength to hypotheses. Rather, tests provide a tool for using incomplete data tolearnabout the process that generated it. This they do, I show, by providing astandardfor distinguishing differences (between observed and hypothesized results) due to accidental or trivial errors from those due to systematic or substantively important discrepancies. I propose a reinterpretation of a commonly used orthodox test to make thislearning modelof tests explicit.

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