Francis Galton “Parent of Modern Statistical Methods”

John Aldrich University of Southampton Centenary Conference September 2011 The phrase comes from Yule’s JRSS obituary of Galton

“As an incidental result of his statistical researches in biology, he was the parent of modern statistical methods”

For Yule, Hon. Secretary of the Statistical Society, the achievement justified the most splendid obituary in the Journal’s history—surpassed only by that for R. A. Fisher 50 years later. “Modern statistical methods” ?

 Yule had just set them out in his Introduction to the Theory of Statistics (1911)

 The main Galton contributions were Univariate analysis—the method of percentiles Bivariate analysis—correlation and regression

Yule was most impressed by the latter: he had extended them to multivariate analysis and developed techniques for association. Had Galton died twenty years earlier in 1891 when he was 69

 the same works would have been celebrated— Hereditary Genius (1869) “Co-relations” (1888) and Natural Inheritance (1889)  but who would have celebrated them?

 The zoologist Raphael Weldon was applying correlation to measurements on crabs and the statistician F. Y. Edgeworth was about to explore implications of correlation. I consider i) how these statistical methods came out of Galton’s biological researches ii) what gave Yule’s appraisal its credibility ______

(i) was largely down to Galton.

(ii) involved others, among them Yule, Weldon and Edgeworth. Galton in his time: statistical physics statistical anthropology/biology, statistical economics and statistical statistics The theory of errors, the best developed branch of applied probability ?

Galton and Maxwell (theory of gases) borrowed from the theory of errors.

But they were not interested in the theory. They were modellers rather than inferential statisticians.

Edgeworth and would extend the inference methods used in the theory to processes of interest to Galton. Galton’s “statistical researches in biology” took off with articles on “Hereditary talent and character” (1865) and a book Hereditary Genius (1869)

Galton (born 1822) was already well-established with reputations as

 African explorer

 Meteorologist

Charles Darwin: relation, colleague and inspiration

 Origin of Species gave 1809-1882 inspiration

 More concretely Variation of Animals proposed a mechanism to account for the facts of inheritance—pangenesis. “In his statistical work Galton may fairly be said to have inherited the mantle of Quetelet” Yule’s comment  refers to Galton’s taking over the normal distribution  but it could be applied to the position of leader—Quetelet had inspired a generation including Galton, Jevons and Nightingale 1796-1874 Hereditary Genius 1869

 I propose to show … that a man’s natural abilities are derived by inheritance, under exactly the same limitations as are the form and physical features of the whole organic world

 Empirical studies of excellence in families make up the bulk of the book

 Concluding chapter has some model-building based on Darwin’s hypothesis of pangenesis Through the 70s—work on Pangenesis

 Experimental work based on Galton's interpretation of the theory as postulating that the gemmules circulate in the blood.  Theoretical papers, “On Blood Relationship” (1872) and “A Theory of Heredity” (1875) revised/extended the theory. Complicated urn models were proposed: An approximate notion of the nearest conceivable relationship between a parent and his child may be gained by supposing an urn containing a great number of balls, marked in various ways, and a handful of them to be drawn out at random as a sample; this sample would represent the person of a parent. Let us next suppose … Typic