American Scientist

To the Editors:

Together with A. W. F. Edwards, I was the last undergraduate student of R. A. Fisher (in genetics in Cambridge, 1956–57). The comment by Hari Dayal and Alok Kalia, and to a lesser extent, the reply by Andrew Gelman (November–December 2009) does a great injustice to Fisher. It is clear that none of the protagonists have read the paragraph in Statistical Methods for Research Workers in which Fisher introduced, in a delightful way, the P < 0.05 level of probability as the threshold that people, who do not understand tests of significance, religiously adhere to. Commenting on his new table of χ2 and probabilities, the two paragraphs on pages 79 and 80 of the first edition (1925) read:

In preparing this table we have borne in mind that in practice we do not want to know the exact value of P for any observed χ2, but, in the first place, whether or not the observed value is open to suspicion. If P is between 0.1 and 0.9 there is certainly no reason to suspect the hypothesis tested. If it is below .02 it is strongly indicated that the hypothesis fails to account for the whole of the facts. We shall not often be astray if we draw a conventional line at .05, and consider that higher values of χ2 indicate a real discrepancy.

To compare values of χ2, or of P, by means of a ‘probable error’ is merely to substitute an inexact (normal) distribution for the exact distribution given by the χ2 table.

Although relating directly to χ2, these comments are generally applicable. Fisher revolutionized experimental science at Rothamsted Experimental Station. By “tackling small sample problems on their merits,” he introduced the concepts and techniques of degrees of freedom, null hypothesis, relevant subset, analysis of variance, an efficient statistic, sufficiency, likelihood, maximum likelihood, test of significance, information, the current standard table of χ2 (with the consequential layout of the other statistical tables that he worked out by pencil and paper methods) and others. Most have a direct application in almost every field of science, engineering, medicine and manufacturing. Thus the comment “To equate agricultural experiments with decisions regarding patients defies logic” is misleading and downright wrong.

David A. Jones, Emeritus
Universities of Hull and Florida