Fisher's Breakthrough

Stephen J Bensman notsjb at LSU.EDU
Fri Jun 3 14:06:57 EDT 2011

As a personal comment to that below, when I told the statistician
guiding my wife and me through Rothamsted and Cambridge about Fisher's
integration below, his eyes opened as wide as hell, and he said, "You
know, you never really do understand this stuff unless you read the
older literature."  So much for the two-year limit imposed by the impact


Stephen J. Bensman

LSU Libraries

Louisiana State University

Baton Rouge, LA  70803




Fisher's linkage of the Lexis Ratio to Pearson's chi-squared test of
goodness of fit through degrees of freedom marked the end of the
theoretical isolation of the British and Continental schools of
statistics from each other.  From a certain perspective, this was
inevitable, because both schools were groping toward the same goals.  In
the "Historical Note," which Fisher (1970) added to the later editions
of his textbook, he pointed out that the chi-squared distribution
originated with the German geodesist, Friedrich Robert Helmert, and was
"rediscovered" (p. 22) by Pearson.  Pearson (1931) himself in an
editorial gave priority to Helmert, suggesting the distribution should
be referred to as "Helmert's Equation" (p. 418).  It appears to be
another case of Stigler's Law of Eponymy, by which "No scientific
discovery is named after its original discoverer" (Stigler, 1980, p.
147; 1999, p. 277).  Fisher's breakthrough enabled the integration of
Lexian statistics into British biometrics.  One of the most important
elements of this integration was the incorporation of the Poisson
process, which had been pioneered by Lexis' student, Bortkiewicz, for
his law of small numbers on the basis of the rate soldiers were kicked
to death by horses in the Prussian Army.  Here it might be pointed out
that British readers-and, from personal experience, others still
today-find Bortkiewicz's example horribly funny.  Thus, Keynes (1922)
commented upon Bortkiewicz's law, "It is startling and even amusing to
be told that horses kick cavalrymen with the same sort of regularity as
characterises the rainfall" (p. 405).  As a result of Fisher's
breakthrough, the way was now open for the development and testing of
the stochastic models that provide the framework for the probability
structure of scientific information.    




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