"In the examples we have given [...] our judgment whether P was small enough to justify us in suspecting a significant difference [...] has been more or less intuitive. Most people would agree [...] that a probability of .0001 is so small that the evidence is very much in favour. . . . Suppose we had obtained P = 0.1. [...] Where, if anywhere, can we draw the line? The odds against the observed event which influence a decision one way or the other depend to some extent on the caution of the investigator. Some people (not necessarily statisticians) would regard odds of ten to one as sufficient. Others would be more conservative and reserve judgment until the odds were much greater. It is a matter of personal taste." (G U Yule & M G Kendall, "An introduction to the theoryof statistics" 14th ed., 1950)
"It will, of course, happen but rarely that the proportions will be identical, even if no real association exists. Evidently, therefore, we need a significance test to reassure ourselves that the observed difference of proportion is greater than could reasonably be attributed to chance. The significance test will test the reality of the association, without telling us anything about the intensity of association. It will be apparent that we need two distinct things: (a) a test of significance, to be used on the data first of all, and (b) some measure of the intensity of the association, which we shall only be justified in using if the significance test confirms that the association is real." (Michael J Moroney, "Facts from Figures", 1951)
"The main purpose of a significance test is to inhibit the natural enthusiasm of the investigator." (Frederick Mosteller, "Selected Quantitative Techniques", 1954)
"Null hypotheses of no difference are usually known to be false before the data are collected [...] when they are, their rejection or acceptance simply reflects the size of the sample and the power of the test, and is not a contribution to science." (I Richard Savage, "Nonparametric Statistics", Journal of the American Statistical Association 52, 1957)
"[...] to make measurements and then ignore their magnitude would ordinarily be pointless. Exclusive reliance on tests of significance obscures the fact that statistical significance does not imply substantive significance." (I Richard Savage, "Nonparametric Statistics", Journal of the American Statistical Association 52, 1957)
"[...] the tests of null hypotheses of zero differences, of no relationships, are frequently weak, perhaps trivial statements of the researcher’s aims [...] in many cases, instead of the tests of significance it would be more to the point to measure the magnitudes of the relationships, attaching proper statements of their sampling variation. The magnitudes of relationships cannot be measured in terms of levels of significance." (Leslie Kish, "Some statistical problems in research design", American Sociological Review 24, 1959)
"There are instances of research results presented in terms of probability values of ‘statistical significance’ alone, without noting the magnitude and importance of the relationships found. These attempts to use the probability levels of significance tests as measures of the strengths of relationships are very common and very mistaken." (Leslie Kish, "Some statistical problems in research design", American Sociological Review 24, 1959)
"The null-hypothesis significance test treats ‘acceptance’ or ‘rejection’ of a hypothesis as though these were decisions one makes. But a hypothesis is not something, like a piece of pie offered for dessert, which can be accepted or rejected by a voluntary physical action. Acceptance or rejection of a hypothesis is a cognitive process, a degree of believing or disbelieving which, if rational, is not a matter of choice but determined solely by how likely it is, given the evidence, that the hypothesis is true." (William W Rozeboom, "The fallacy of the null–hypothesis significance test", Psychological Bulletin 57, 1960)
"The null hypothesis of no difference has been judged to be no longer a sound or fruitful basis for statistical investigation. […] Significance tests do not provide the information that scientists need, and, furthermore, they are not the most effective method for analyzing and summarizing data." (Cherry A Clark, "Hypothesis Testing in Relation to Statistical Methodology", Review of Educational Research Vol. 33, 1963)
"[...] the test of significance has been carrying too much of the burden of scientific inference. It may well be the case that wise and ingenious investigators can find their way to reasonable conclusions from data because and in spite of their procedures. Too often, however, even wise and ingenious investigators [...] tend to credit the test of significance with properties it does not have." (David Bakan, "The test of significance in psychological research", Psychological Bulletin 66, 1966)
"[...] we need to get on with the business of generating [...] hypotheses and proceed to do investigations and make inferences which bear on them, instead of [...] testing the statistical null hypothesis in any number of contexts in which we have every reason to suppose that it is false in the first place." (David Bakan, "The test of significance in psychological research", Psychological Bulletin 66, 1966)
"Significance levels are usually computed and reported, but power and confidence limits are not. Perhaps they should be." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
"The emphasis on significance levels tends to obscure a fundamental distinction between the size of an effect and its statistical significance." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
"[...] too many users of the analysis of variance seem to regard the reaching of a mediocre level of significance as more important than any descriptive specification of the underlying averages. Our thesis is that people have strong intuitions about random sampling; that these intuitions are wrong in fundamental respects; that these intuitions are shared by naive subjects and by trained scientists; and that they are applied with unfortunate consequences in the course of scientific inquiry. We submit that people view a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics. Consequently, they expect any two samples drawn from a particular population to be more similar to one another and to the population than sampling theory predicts, at least for small samples." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)
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