The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives

22. How the Wasp Stung the Bee and Took over Some Sciences

22 How the Wasp Stung the Bee and Took over Some Sciences How long does a wasp take in loading herself with sweets? edgeworth 1896, 358 In 1922 Fisher wrote to Gosset, soliciting Gosset’s new table of t. Fisher was eager to put the updated table in the first edition of his Statistical Methods for Research Workers. They would call Gosset’s tables “the table of ‘Student’s’ t,” in celebration of Fisher’s correction to Gosset’s 1908 table of z. Gosset, as always, wanted to help. He was unusually busy with work at the brewery. Baby Triumphator, his calculator, he told Fisher, was needed for overtime work.1 Calculating t-values at various levels of significance as N goes from small to large was difficult manual labor. Gosset ’s own assistant, E. M. Somerfield (aka “Mathetes”), himself a Fisher student and an accomplished statistician, was not strong enough to turn the handle.2 Fisher would have to wait. Fisher’s tone in reply was urgent. So Gosset put Somerfield onto the task of preparing the index to Fisher’s book. That freed some time for Gosset —who was planning himself to help with the index to the anti-Gosset book—to turn the crank on Baby Triumphator. When he sent the new t-values to Fisher, in September 1922, Gosset exclaimed with deficient foresight , “[y]ou are the only man that’s ever likely to use them!”3 The men discovered some errors in the 1922 version and went back to work. But Fisher then asked Gosset if he could “quote” the completed table in a Biometrika article Fisher contemplated. “Dear Fisher,” Gosset replied in July of 1923, “I expect to finish it sometime next winter. I should say that it is certainly in course of preparation. As to ‘quoting’ the table in Biometrika it depends 227 just what you mean by quoting. . . . I don’t think, if I were Editor, that I would allow much more than a reference!”4 For over a year they worked out the bugs in the table, Gosset doing most of the work. The Sting In Student’s name the original table of z had first been copyrighted, in 1908, in Pearson’s Biometrika. A second version was published by Student in Karl Pearson’s Tables for Biometricians and Statisticians (1914). A third, fuller version of z (with more n) was copyrighted by Student in 1917, also in the Pearson-edited journal (Student 1908a, 1917). Fisher in the early 1920s published “small sample” results in the Italian journal Metron, edited by Corrado Gini, first in 1921 and a second time in 1924 (Fisher 1950, 1.2a). By 1925 the Wasp had cocked his stinger. Fisher published two articles in the December 1925 issue of Metron, “Applications of ‘Student’s’ Distribution” and “Expansion of ‘Student’s’ Integral in Powers of n⫺1” (1925b, 1925c). Sandwiched between Fisher’s two articles was a much shorter article (a little over three pages long), by Student himself, “New Tables for Testing the Significance of Observations ” (1925). Student wrote, “The present Tables have . . . at Mr. Fisher’s suggestion been constructed with argument t ⫽ z  n where n is now one less than the number in the sample, which we may call n⬘” (106). The balance of Gosset’s article explains in detail how Gosset calculated the t-tables. Fisher’s first article, at fourteen pages long—he apologized in a letter to Gosset for excess length but went on to say that it should be longer yet—is by contrast rhetorically complicated and didactic, as Fisher was. His “Applications” demonstrates in n-dimensional Euclidean space what remains to Gosset “partly intuitive” (Fisher 1925b, 92)—the “exactitude of ‘Student’s’ distribution for normal samples” (92). He then illustrates “significance of differences between means”—showing how “‘Student’s’ distribution affords the solution to a variety of problems beyond that for which it was originally prepared” (94–96). He goes on to show—and this was truly novel, another Gosset-inspired idea—“the second class of tests for which ‘Student’s’ distribution provides an exact solution , . . . testing the significance of the large class of statistics known as regression coefficients” (96; Lehmann 1999; italics supplied). Unsurprisingly significance rules: “The multiple correlation must be judged significant,” Fisher declares, “only if the value of P obtained is too small to allow us to admit the hypothesis that the dependent variate is re228 ⱐ The Cult of Statistical Significance ally uncorrelated with the independent...