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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]

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