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. 
Category Archive: .Meehl, Paul E.
Contrast this bizarre state of affairs with the state of affairs in physics. While there are of course a few exceptions, the usual situation in the experimental testing of a physical theory at least involves the prediction of a form of function (with parameters to be fitted); or, more commonly, the prediction of a quantitative magnitude (point-value). Improvements in the accuracy of determining this experimental function-form or point-value, whether by better instrumentation for control and making observations, or by the gathering of a larger number of measurements, has the effect of narrowing the band of tolerance about the theoretically predicted value. What does this mean in terms of the significance-testing model? It means: In physics, that which corresponds, in the logical structure of statistical inference, to the old-fashioned point-null hypothesis H0 is the value which flows as a consequence of the substantive theory T; so that an increase in what the statistician would call “power” or “precision” has the methodological effect of stiffening the experimental test, of setting up a more difficult observational hurdle for the theory T to surmount. Hence, in physics the effect of improving precision or power is that of decreasing the prior probability of a successful experimental outcome if the theory lacks verisimilitude, that is, precisely the reverse of the situation obtaining in the social sciences.
As techniques of control and measurement improve or the number of observations increases, the methodological effect in physics is that a successful passing of the hurdle will mean a greater increment in corroboration of the substantive theory; whereas in psychology, comparable improvements at the experimental level result in an empirical test which can provide only a progressively weaker corroboration of the substantive theory.
In physics, the substantive theory predicts a point-value, and when physicists employ “significance tests,” their mode of employment is to compare the theoretically predicted value x0 with the observed mean x0, asking whether they differ (in either direction!) by more than the “probable error” of determination of the latter. Hence H : H0 = μx functions as a point-
Inadequate appreciation of the extreme weakness of the test to which a substantive theory T is subjected by merely predicting a directional statistical difference d > 0 is then compounded by a truly remarkable failure to recognize the logical asymmetry between, on the one hand, (formally invalid) “confirmation” of a theory via affirming the consequent in an argument of form: [T ⊃ H1, H1, infer T], and on the other hand the deductively tight refutation of the theory modus tollens by a falsified prediction, the logical form being: [T ⊃ H1, ~H1, infer ~T].
While my own philosophical predilections are somewhat Popperian, I daresay any reader will agree that no full-fledged Popperian philosophy of science is presupposed in what I have just said. The destruction of a theory modus tollens is, after all, a matter of deductive logic; whereas that the “confirmation” of a theory by its making successful predictions involves a much weaker kind of inference. This much would be conceded by even the most anti-Popperian “inductivist.” The writing of behavior scientists often reads as though they assumed—what it is hard to believe anyone would explicitly assert if challenged—that successful and unsuccessful predictions are practically on all fours in arguing for and against a substantive theory. 
Isn’t the social scientist’s use of the null hypothesis simply the application of Popperian (or Bayesian) thinking in contexts in which probability plays such a big role? No, it is not. One reason it is not is that the usual use of null hypothesis testing in soft psychology as a means of “corroborating” substantive theories does not subject the theory to grave risk of refutation modus tollens, but only to a rather feeble danger. The kinds of theories and the kinds of theoretical risks to which we put them in soft psychology when we use significance testing as our method are not like testing Meehl’s theory of weather by seeing how well it forecasts the number of inches it will rain on certain days. Instead, they are depressingly close to testing the theory by seeing whether it rains in April at all, or rains several days in April, or rains in April more than in May. [821-2]