Francis Galton “Parent of Modern Statistical Methods”

John Aldrich University of Southampton Francis Galton 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 wereUnivariate analysis—the method of percentilesBivariate 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 Karl Pearson 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 inspiration

More concretely Variation of Animals proposed a mechanism to account for the facts of inheritance—pangenesis.

1809-1882

“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 …

Typical Laws of Heredity 1877—reversion

Data on sweet peas.

Inheritance modelled as a stable first order autoregressive process.

Galton gave Jevons a parallel in political economy: “the successive stages by which overproduction of any commodity reverts to one of normal production.”

Galton and the statisticians

The Statistical Society promoted “the collection and comparison of Facts which illustrate the condition of mankind, and tend to develop the principles by which the progress of society is determined.”

Galton joined in 1860, was on the Council from 1869 to 79, contributed a paper to the Jubilee celebrations in 1885 but contributed only 3 papers to the Journal.

Only one of Galton’s methodological papers treated the Statistical Society’s statistics: “The geometric mean in vital and social statistics” (1879) published in the Proceedings of the Royal Society.

Fellow-spirits among the statisticians?

W. S. Jevons (died 1882)

F. Y. Edgeworth joined the Society in 1881

Big gap till

Bowley (a follower of Edgeworth) in 1894

Yule in 1896 and further Pearsonians after 1900

Galton’s books were not reviewed in the JRSS.

The mathematical utilitarian F. Y. Edgeworth had noticed Hereditary Genius

What sort of people do we want?

When people vary in their ability to produce happiness, we choose those who are best at producing happiness.

A eugenic objective before there was a eugenics movement

Edgeworth then took up statistics

Not the arithmetical portion of social science

But the science of Means in general …or the science of those Means which relate to social phenomena

He was led to rework Laplace, Quetelet, Galton, …

Natural Inheritance–distillation of 20 yearsMain questions

“The large do not always beget the large, nor the small the small and yet the observed proportion between the large and the small … hardly varies from one generation to another.” Why?

“A second problem regards the average share contributed to the personal features of the offspring by each ancestor severally.”“The question I have to solve, in a reasonable and not merely in a statistical way, is, how much less?”

Galton’s paper on correlation had more impact than the book

Edgeworth developed the mathematical theory and discussed statistical applications

Weldon took correlation into biology

Like reversion/regression this exploited facets of the bivariate normal.

Walter Frank Raphael Weldon

Professor of zoology at University College

Starts using Galtonian methods in 1890—percentiles first and then correlation

Encouraged and helped by Galton

Not a prolific publisher

Left no school1860-1906

If Galton had died in 1891…

Edgeworth and Weldon would have celebrated his statistical methods

The philosopher John Venn had also paid Galton some attention.

But there would have been no Yule obituary

For that Karl Pearson was required.

Karl Pearson applied mathematician and philosopher of science

1891 begins working with Weldon

1893 starts teaching statistics with Yule in the first class

…

1911 Galton Professor of National Eugenics

1914-30 publishes Life, Letters and Labours of Francis Galton

1857-1936

Pearson without Galton

Pearson’s first two “Contributions to the Theory of Evolution” 1894/6 treat estimating a mixture of normals and introduce the Pearson curves.

In 1889 he had read Galton’s Natural Inheritance but was not impressed

When Pearson took up with Weldon Edgeworth was an important guide and main influence

Pearson re-writing Natural Inheritance

These papers focussed on Galton and brought heavy mathematical machinery to bear on his ideas.

Yule was the first Pearsonian

to join the Statistical Society

His first paper introduced the Pearson curves to social statistics.

Later papers applied correlation and regression to social problems

Regression was no longer a process but a way of presenting multivariate data

When Yule took the new statistical methods to the Society Galton was their

Galton told statisticians of their “large debt of

gratitude to University College for the variety of statistical investigations carried on there, both mathematical and experimental.”

Later Yule wrote, “No younger man who came into personal contact with him is likely to forget his friendly and utterly unassuming discussion— as between equals—of any points that might arise.”

Was a new journal needed?

Pearson contemplated a journal “of pure and applied statistics” but had "found a feeling pretty general that it might injure the R.S.S. Journal, although the sort of memoirs I had in view would I think not find a place in that journal.”

In 1901 the need came from a crisis in publishing Pearson’s statistical biology in the Royal Society’s publications.

Galton backed Pearson and Weldon morally and financially

Join the Editorial Committee? Yes“if it could be done in a way that both in reality and in the eyes of the public it carried no more responsibility and work than the position of ‘Consulting Physician’ does in a Hospital.”

Retrospective I: Galton on Galton

it seemed most desirable to obtain data that would throw light on the Average contribution of each Ancestor to the total heritage of the offspring in a mixed population

This is a purely statistical question, the same answer to which would be given on more than one theoretical hypothesis of heredity, whether it be Pangenetic, Mendelian or other.

Autobiography 1908

A change, a surrender …?

In Natural Inheritance “The question I have to solve, in a reasonable and not merely in a statistical way, is, ..”

By 1908 “theoretical hypotheses” had been elaborated and Galton wanted to save his research

Galton’s methodological position seemed close to Pearson (1896)

the formulae make not the least pretence to explain the mechanism of inheritance. All they attempt is to provide a basis for the quantitative measure of inheritance—a schedule, as it were, for tabulating and appreciating statistics.

Retro II Yule on Galton—Obituary 1911

Yule wrote for a new generation interested in the statistical study of statistical problems

The Pearsonians—David Heron (born 1881), Major Greenwood (born 1880) and Ernest Snow (born 1886)

The economists—Arthur Bowley (born 1869), Charles Sanger (born 1872) and Maynard Keynes (born 1883)

Reginald Hooker (born 1867) Yule’s collaborator.

Retrospective III Pearson on Galton

As Pearson worked on the Life his view of Galton’s significance changed and his view of how Galton had influenced him changed too.

For example in 1934 Pearson claimedIt was Galton who first freed me from the prejudice that sound mathematics could only

be applied to natural phenomena under the category of causation.

When did Galton free him?

But the escape from causation only became an issue for Pearson in 1910.In the third edition of the Grammar of Science he claimed:

It is this conception of correlation between two occurrences embracing all relationships from absolute independence to complete dependence, which is the wider category by which we have to replace the old idea of causation.

Because it’s Galton

I finish with a pedigree and an assessment of parental contributions.

My sense is that in statistics Galton had no independent influence on his descendents’ descendents—the influence came through the descendents…

Pedigrees: biometricians & statisticians

The “theory of errors” kept influencing developments on the left without being influenced by them

Galton affected all his successors on the left

But there was no separate ancestral contribution

Galton was transmitted through Pearson and Edgeworth

Fisher’s first paper was published in 1912..

Galton influences on modern statistics may come through other routes—e.g. his map- making on modern statistical graphics.

Theory

of

errors

Yule

Fisher

Bowley

Galton

Darwin

Pearson

Edgeworth

Quetelet