Category Archive: “The Problem Is Epistemology, Not Statistics”

[Harlow, Lisa L. et al. (eds.): What If There Were No Significance Tests? Erlbaum: 1997.]

Weak statistical tests

The distinction between the strong and the weak use of significance tests is logical or epistemological; it is not a statistical issue. The weak use of significance tests asks merely whether the observations are attributable to “chance” (i.e., no relation exists) when a weak theory can only predict some sort of relation, but not what or how much. The strong use of significance tests asks whether observations differ significantly from the numerical values that a strong theory predicts, and it leads to the fourth figure of the syllogism—p ⊃ q, ~q , infer ~p—which is formally valid, the logician’s modus tollens (“destroying mode”). Psychologists should work hard to formulate theories that, even if somewhat weak, permit derivation of numerical point values or narrow ranges, yielding the possibility of modus tollens refutations. [422]

The problem is epistemology, not statistics

Significance tests have a role to play in social science research but their current widespread use in appraising theories is often harmful. The reason for this lies not in the mathematics but in social scientists’ poor understanding of the logical relation between theory and fact, that is, a methodological or epistemological unclarity. Theories entail observations, not conversely. Although a theory’s success in deriving a fact tends to corroborate it, this corroboration is weak unless the fact has a very low prior probability and there are few possible alternative theories. The fact of a nonzero difference or correlation, such as we infer by refuting the null hypothesis, does not have such a low probability because in social science everything correlates with almost everything else, theory aside. In the “strong” use of significance tests, the theory predicts a numerical point value, or narrow range, so the hypothesis test subjects the theory to a grave risk of being falsified if it is objectively incorrect. In general, setting up a confidence interval is preferable, being more informa­tive and entailing null hypothesis refutation if a difference falls outside the interval. Significance tests are usually more defensible in technological contexts (e.g., evaluating an intervention) than for theory appraisal. [393]