Tag Archive: falsifiability

The real Popper

It is worth noting that even in Lakatos’s own “methodology of scientific research programmes” (“MSRP”)—a type of sophisticated methodological falsificationism that Lakatos presents as the crowning synthesis of the “thesis” dogmatic falsificationism and the “antithesis” naive methodological falsificationism—the test statements and interpretative theo­ries still are accepted on the basis of a research program. So Lakatos gives a conventionalist solution to the problem of how basic statements are selected, in his interpretation of Popper’s methodology and in his own methodology as well.

This interpretation of Popper is not correct, and the suggested conventionalist solution to the problem of how test state­ments are accepted is not satisfying. Popper’s criticist solution, which Lakatos has not correctly understood, is much better and is also a solution that allows us to understand the history of science better than Lakatos’s oversophisticated combination of conventionalism and falsificationism. Lakatos maintains that sophisticated methodological falsifica­tionism combines the best elements of voluntarism, pragmatism, and the realist theories of empirical growth. Critical falsificationism is better still, among other reasons because it avoids that kind of eclecticism. And for those interested in the history of ideas, it might be worthwhile to know that the real Popper is neither a dogmatic falsificationist nor a naive or sophisticated methodological falsificationist. Not only Popper0 but also Popper1 and Popper2 are myths created by a misunderstanding of Popper’s critical falsificationism.[53]

Falsification as conditional disproof

Kuhn asked what falsification is, if not conclusive disproof. The answer is that falsification is a conditional disproof, conditional on the truth of the used test statements (and in some cases also on the truth of some used auxiliary hypotheses). Feyerabend’s example of the alleged falsification of the Copernican system with naked-eye observations shows this conditional character of falsifications quite well.

Does this cause any logical or methodological problems? The logical situation is quite clear and unproblematic. The methodological situation is only problematic for those who assume that there are infallible test statements. But as Kuhn said, Popper stresses that test statements are fallible. [56]

The myth of naive falsificationism

Naive falsificationism is a myth created by positivist and conventionalist misunderstandings of Popper’s methodology. In the contemporary methodological discussion it is time to end the discussion of the straw man of naive falsificationism in its different positivist and conventionalist variants. It is time to come back to reality and to begin a discussion of real and critical falsificationism. [62]

Fisher’s severe tests

In choosing the grounds upon which a general hypothesis should be rejected, the exprimenter will rightly consider all points on which, in the light of current knowledge, the hypothesis may be imperfectly accurate, and will select tests, so far as possible, sensitive to these possible faults, rather than to others. [47]

Fisher on the logic of null hypotheses

In relation to any experiment we may speak of this hypothesis as the “null hypothesis,” and it should be noted that the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every ex­periment may be said to exist only in order to give the facts a chance of disproving the null hypothesis.

It might be argued that if an experiment can disprove the hypothesis that the subject possesses no sensory discrimi­nation between two different sorts of object, it must therefore be able to prove the opposite hypothesis, that she can make some such discrimination. But this last hypothesis, however reasonable or true it may be, is ineligible as a null hypothesis to be tested by experiment, because it is inexact. If it were asserted that the subject would never be wrong in her judgements we should again have an exact hypothesis, and it is easy to see that this hypothesis could be dis­proved by a single failure, but could never be proved by any finite amount of experimentation. [16]

Fisher on significance tests

In considering the appropriateness of any proposed experimental design, it is always needful to forecast all possible results of the experiment, and to have decided without ambiguity what interpretation shall be placed upon each one of them. Further, we must know by what argument this interpretation is to be sustained. …

It is open to the experimenter to be more or less exacting in respect of the smallness of the probability he would require before he would be willing to admit that his observations have demonstrated a positive result. It is obvious that an experiment would be useless of which no possible result would satisfy him. Thus, if he wishes to ignore results having probabilities as high as 1 in 20—the probabilities being of course reckoned from the hypothesis that the phenomenon to be demonstrated is in fact absent … . It is usual and convenient for the experimenters to take 5 per cent. as a standard level of significance, in the sense that they are prepared to ignore all results which fail to reach this standard, and, by this means to eliminate from further discussion the greater part of the fluctuations which chance causes have intro­duced into their experimental results. No such selection can eliminate the whole of the possible effects of chance co­incidence, and if we accept this convenient convention, and agree that an event which would occur by chance only once in 70 trials is decidedly “significant”, in the statistical sense, we thereby admit that no isolated experiment, how­ever significant in itself, can suffice for the experimental demonstration of any natural phenomenon; for the “one chance in a million” will undoubtedly occur, with no less and no more than its appropriate frequency, however surprised we may be that it should occur to us. In order to assert that a natural phenomenon is experimentally demonstrable we need, not an isolated record, but a reliable method of procedure. In relation to the test of significance we may say that a pheno­menon is experimentally demonstrable when we know how to conduct an experiment which will rarely fail to give us a statistically significant result. [12-4]

So you did one study? Do some more.

If one in twenty does not seem high enough odds, we may, if we prefer it, draw the line at one in fifty (the 2 per cent. point), or one in a hundred (the 1 per cent. point). Personally, the writer prefers to set a low standard of significance at the 5 per cent. point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance. The very high odds sometimes claimed for experimental results should usually be discounted, for inaccurate methods of esti­mating error have far more influence than has the particular standard of significance chosen. [504-5]

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]

Inductive psychology vs deductive physics

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-null hypothesis, and the prior (logical, antecedent) probability of its being correct in the absence of theory approximates zero. As the experimental error associated with our determination of x0 shrinks, values of x0 consistent with x0 (and hence, compatible with its implicans T) must lie within a narrow range. In the limit (zero probable error, corresponding to “perfect power” in the significant test) any non-zero difference (x0 – x0) provides a modus tollens refutation of T. If the theory has negligible verisimilitude, the logical probability of its surviving such a test is negligible. Whereas in psychol­ogy, the result of perfect power (i.e., certain detection of any non-zero difference in the predicted direction) is to yield a prior probability p = ½ of getting experimental results compatible with T, because perfect power would mean guaranteed detection of whatever difference exists; and a difference [quasi] always exists, being in the “theoretically expected direc­tion” half the time if our substantive theories were all of negligible verisimilitude (two-urn model). [112-3]

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