Fisher vs. Pearson

[Stephen J Bensman]

More fun from the book.  A number of you have stated that you like these sendings.  That below is not only of intrinsic interest but contains the following lesson:  When it comes to skewering each other, the Brits are the best, and you should never get on the wrong side of one, particularly, if he/she is also a poet.  That would be double indemnity.

 

Stephen J. Bensman

LSU Libraries

Louisiana State University

Baton Rouge, LA   70803

USA

notsjb at lsu.edu

 

In order to understand R. A. Fisher's theoretical advances in statistics, it is necessary to have a grasp of his overall career and personality.  Born in 1890, he attended Cambridge, where he passed the Mathematical Tripos as a Wrangler with distinction in 1912.  While at Cambridge he read very carefully and critically Karl Pearson's "Mathematical Contributions to the Theory of Evolution," (Mahalanobis . 1938).  This was the beginning of what Fisher later stated was a "prolonged...lifelong study of Pearson's writings and their effect upon the development of modern statistics" (Edwards, 1994, p. 105).  As another sign of his future direction it was at Fisher's instigation that Cambridge University Eugenics Society was formed in 1911 (J. F. Box, 1978, pp. 26-28; 1983, p. 104).  Throughout his career, Fisher was focused on biological research, and here he can be considered as having laid the modern foundations in three areas: 1) statistical theory and techniques; 2) experimental design; and 3) mathematical genetics.  In 1919 Fisher obtained his first employment after graduating from Cambridge in a new, at first temporary post, as statistician at the Rothamsted Experimental Station, where agricultural research had been taking place since 1843.  Yates and Mather (1963, p. 92), both of whom were close associates of Fisher, speculate that one reason he accepted the Rothamsted post was the prospect it offered to pursue his genetic studies.  However, Fisher's main achievement there was to develop statistical and experimental methods applicable to practical research in agricultural.  Fisher summed up his research in statistics in his textbook Statistical Methods for Research Workers that was published in 14 editions from 1925 to 1970.  Yates and Mather (1963) state that in this textbook Fisher made a considerable effort to make the new statistics understandable to practical workers who wished to use them, limiting it essentially to a compilation of methods without mathematical proofs.  However, they describe its first 1925 edition as a "tour de force" (p. 105), and, given Fisher's phenomenal grasp of the field and use of datasets that played important roles in statistical advances as explanatory examples, it is important source for understanding the historical development of statistical theory and methods.  Fisher summarized his experimental methodology in The Design of Experiments, which was published in seven editions from 1935 to 1960.  Yates and Mather (1963, pp.94 and 113) state that this was the first book explicitly devoted to this subject, and  it amplified and extended the somewhat cursory and elementary exposition of this topic in Statistical Methods.   Design of Experiments was also not mathematical but a discussion of the basic logical principles of experimentation, and it opens with the famous experiment conducted by Fisher shortly after he arrived at Rothamsted to test the assertion of a lady scientist, B. Muriel Bristol, that she could tell by the taste whether the tea or the milk had been poured into the cup first.  Fisher's daughter, J. F. Box (1978, p. 134), reports in her biography of her father, that, although never reported, Bristol not only passed the test but so impressed the male scientist, who helped Fisher set up the experiment, that he married her.  In his book entitled The Lady Tasting Tea Salsburg (2001, pp. 1-8) reports that he was told in the late 1960s by H. Fairfield Smith, who had personally witnessed the experiment, that Bristol got every cup right, thereby ending any question of probability and possibly preventing Fisher from stating the actual results of the experiment in his book.

            In the assessment of Yates and Mather (1963, p. 120) Fisher never held the dominant position in genetics that he did in statistics.  Yet all his academic positions were in the former discipline and never in the latter.  This caused Kendall (1963) to comment wryly, "It is remarkable that the greatest statistician in the world never held a chair in statistics" (p. 5).  When Karl Pearson retired from University College London in 1933, the Department of Applied Statistics, which he chaired-the first university statistics department in the world-was split into the Department of Eugenics and the Department of Statistics.  Fisher was hired as the head of the Department of Eugenics, whereas Pearson's son, Egon, took over the Department of Statistics.  In 1943 Fisher was elected to the Balfour Chair of Genetics at Cambridge University, which can be considered his last truly academic post.  Fisher's main achievements in genetics have been succinctly described by Mather (1963; see also Yates and Mather, 1963, pp. 113-120).  According to Mather (1963), Fisher's great contributions were to the theory and structure of the science, and of these two were outstanding.  The first was made by Fisher (1918) early in his career in an article entitled "The Correlation between Relatives on the Supposition of Mendelian Inheritance," whose significance is set forth by Mather (1963) thus:

   ...In this he showed, for the first time, not only that Galton's and Pearson's 

   findings about continuous variation in such characters as human stature were

   fully compatible with Mendel's principles, but, what was more important, 

   that the correlations between relatives could be made to yield information

   about such properties as dominance of the genes involved.  It was 14 years 

   before he followed this up..., and it has always seemed remarkable to me that 

   he, of all people the most eminently fitted to develop this fusion of biometry 

   and genetics, wrote in fact so little about it. Even so, to Fisher more than to

   anyone else we owe the foundation of what we have come to call biometrical 

   genetics. Others had seen the problem: Fisher showed us how to solve it. 

   Others had seen the prospective reconciliation of biometry and Mendelism: 

   Fisher brought them together, and in doing so gave us a methodology which

    basically we still use.  p. 167. 

Fisher's other outstanding contribution, according to Mather (1963), was to resolve the 

issue of evolutionary gradualism vs. saltation dividing the biometrical and Mendelian 

schools.  Fisher (1930) did this in a book entitled The Genetical Theory of Natural 

Selection, of which Mather (1963) gave the following evaluation:

   ...Bateson and the early geneticists had felt their findings to be incompatible

     with the principle of evolution by natural selection and especially with the

     significance Darwin attached to small variations in adaptation and evolution. 

     By the 1920's a number of geneticists were pointing out that this was not so; 

     that, far from being incompatible, Darwinism and Mendelism were, in fact,  

     complementary. Fisher's contribution was basic, characteristic and unique. It is 

      set out in The Genetical Theory of Natural Selection. He pointed out that natural  

      selection is not evolution, that in fact evolution is but one manifestation of the  

     operation of natural selection, and that natural selection can and should be studied

      in its own right. Having delimited his field, he proceeded to cultivate it as only he 

      could...  Again he went beyond merely harmonizing, to fusing the principles of 

      genetics and natural selection.  pp. 167-168.  

Thus, Fisher ended the schism between the biometrical and Mendelian schools, laying the foundations of the modern discipline of biometrical genetics.

            Fisher is credited with having almost single-handedly created the foundations of modern statistics.  MacKenzie  (1981) regards his work as marking the start of the present day, stating, "Fisher's statistical theories and methods still form the basis of much contemporary teaching and research" (p. 10).  However, he left a confusing legacy.  This was primarily due to two factors.  First, he had difficulty in expressing himself clearly, and this is brought out by the following assessment of his textbook Statistical Methods for Research Workers by Kendall (1963):

   ...It is not an easy book. Somebody once said that no student should

    attempt to read it unless he had read it before. Fisher had no gifts of 

    exposition, even of his own ideas, and rarely set out explicitly the 

    assumptions on which he was working.  p.2 

This particularly affected Fisher's writings on inference, which Bartlett (1965) described as "extremely cryptic" (p. 397).  Cochran (1967) once declared, "I have difficulty in understanding exactly what Fisher meant by a test of significance: he seems to imply different things in different parts of his writings" (p. 1461).

            The second factor confusing his legacy was his pugnacious character.  In this he resembled the person, of whom he is considered the direct descendant and who became one of his bêtes noires-Karl Pearson.  Irwin (1963) gave the following assessment of the personalities of the two men:  

      I am now, I believe, the only surviving person who was on both Karl

Pearson's staff and R. A. Fisher's staff at Rothamsted. Both men were 

  scientific giants; both were polymaths. Both inspired the most fervent 

   devotion in their own staffs-and deservedly. Both were intolerant 

   of points of view in mathematical statistics other than their own. In 

   both cases this led to a selective tendency to quarrel with some other, 

  but not all, mature intellects. Certainly both were entirely unconscious of 

   the fact that they were not being completely objective in such cases.  p. 161 

According to Irwin, the only difference was that, with the conspicuous exception of Bateson, Pearson quarreled temporarily with many people, whereas Fisher never reconciled with anybody.  In a book, which Kendall (1963, p. 6) wished would have never been written, Fisher (1973) delivered himself of a string of ferocious insults against Pearson, which started off with the statement: "The terrible weakness of his mathematical and scientific work flowed from his incapacity in self-criticism, and his unwillingness to admit the possibility that he had anything to learn from others, even in biology, of which he knew very little" (p. 3).  Kendall (1963) wrote of this passage:  

...In his last book...he gives a sketch of K. P. and renews his attack 'on

    the whole corpus of Pearsonian writings'. And the strangest thing of 

   all is that the faults of which he accused Pearson were ones which 

   can be detected in Fisher himself. 'He reminds me', said a Dutch 

   colleague, 'of one of those artists who, whenever they paint a portrait, 

   paint a self-portrait.'  p.. 3.

In a biography of Pearson, which he was mistakenly asked to write for the authoritative Dictionary of National Biography and could not be published for obvious reasons, Fisher summed up the biometrician vs. Mendelian controversy, whose main protagonists were Bateson and Pearson, thus:  "The controversy proved nothing, but that Bateson did not know enough of mathematics, nor Pearson enough of biology" (Edwards, 1994, p. 103).  The final conclusion to be reached from this on Fisher is the following one reached by Gridgeman (1972):  "His mastery of the elegantly barbed phrase did not help dissolve feuds, and he left a legacy of unnecessary confusion in some areas of statistical theory" (p. 8).

 

 

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