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\noindent{\bf Francis GALTON}\\
b. 16 February 1822 -- d. 17 January 1911
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{\bf Summary.} Francis Galton developed the basic statistical concepts of
regression
lines and correlation between variables. He helped in founding the
journal {\it Biometrika} and left most of his fortune to establish
the Chair of
Eugenics subsequently occupied by K. Pearson and R.A. Fisher.
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Francis Galton was born in Birmingham (England) and died in
Haslemere (England). His grandfathers Erasmus Darwin and Samuel
Galton were both members of an informal society of scientists,
inventors, and industrialists that is known as the Lunar Society
of Birmingham as its meetings were held on nights of the full
moon. Other members included Matthew Boulton, Richard Lovell
Edgeworth, Joseph Priestley, James Watt, and Josiah Wedgwood.
The children and grandchildren of members of this society tended
to marry one another. In particular, Samuel Tertius Galton, the
second son of Samuel Galton married Frances Anne Violetta Darwin,
the eldest daughter of Erasmus Darwin by his second marriage.
Thus Charles Darwin and Francis Galton were first cousins.
Francis Galton was also related by marriage to Francis Ysidro
Edgeworth (q.v.), a grandson of Richard Lovell Edgeworth, as
Galton's wife's brother, Arthur Gray Butler, married Edgeworth's
first cousin, Harriet Jessie Edgeworth. Another brother, Henry
Montagu Butler was Master of Trinity College, Cambridge, when
Galton was elected an Honorary Fellow of the College in 1902. For
a detailed account of the ramifications of this type of social
grouping (sometimes known as an `intellectual aristocracy') in
the subject areas of statistics and eugenics, see McKenzie
(1981).
Galton's father and grandfather were both prosperous gun
manufacturers and bankers (despite their also being members of
the Society of Friends or Quakers). Nevertheless Galton intended
to follow Erasmus Darwin and his Darwin uncles into a medical
career. He began his medical training at the Birmingham General
Hospital in 1838 and continued it at King's College, London, in
1839, but broke his training off to study mathematics at Trinity
College, Cambridge, in 1840. However, poor health obliged him to
abandon the honours course and take a `poll' or pass degree in
1844.
Galton's father died in 1844 leaving his third son (and youngest
child) a substantial income. He abandoned any thought of a
medical career and gave himself up to amusements for a period of
five years, but this style of life was not able to satisfy his
ambition.
In his student days Galton had travelled widely in the territory
of the Ottoman Empire. On one trip he had visited Vienna,
Constantinople (then the capital of the Empire), and Smyrna, and
on a second he had travelled in Egypt and Syria.
In 1850 Galton mounted an expedition at his own expense, but
under the aegis of the Royal Geographical Society, to
the little-known Territory of Damaraland in South-West Africa (now Namibia).
He Landed at Walfisch or Walvis Bay and penetrated into the
interior. On his return to England in 1852, he wrote an account
of his expedition entitled {\it Tropical South Africa} (1853)
and a practical guide to {\it The Art of Travel} (1853) which
is still in print.
Galton was elected a Fellow of the Royal Society of London in
1856 and frequently served on the council of the Society. He was
active in the British Association for the Advancement of Science
and Served as General Secretary of the Association 1863-67. In
1863 he published a book entitled {\it Meteorographica, or
Methods of Mapping the Weather}, which led to his serving as a
member of the Governing Council of the British Meterological
Office 1868-1900. The term `anticyclone' was introduced by him.
In his {\it Hereditary Genius} (1869) he developed the
argument that the descendents of eminent persons are more likely
to be `eminent' than others, though to a lesser degree than their
immediate ancestors. A difficulty in defining such abstract
concepts as `eminence' obliged him to turn his attention to
physical measurements, and in 1884 Galton set up an
Anthropometric Laboratory in connection with the International
Health Exhibition of 1884-85 in which he took physical
measurements of individuals who presented themselves. Some of the
results of these experiments are presented in his {\it Natural
Inheritance} (1889).
With his social background, his interests in heredity, and in the
context of the ideas on natural selection discussed by Darwin and
Huxley, it is not surprising to find that Galton believed in the
superiority of certain human types. He recommended breeding from
the `best' social types and restricting the offspring of the
`worst'. He coined the term `eugenics' (though not the name
Eugene). He devoted much of his income in later life to the
promotion of this subject and, after his death, he bequeathed
most of his estate to University College, London, to found a
Chair of Eugenics. Karl Pearson (q.v.) and Ronald Fisher (q.v.)
were the first two holders of this chair. Pearson (1914-30)
naturally included extensive genealogical tables of the Galton
family in his three volume biography of Francis Galton.
Galton's statistical work began well before 1885, but, because
it contents are relatively familiar, it is convenient to begin
our account of his work in this area with his 1885 paper
published in the {\it Philosophical Transactions of the Royal
Society.} In this paper he compiled a table of the heights of
928 adult individuals and the weighted average of their parents'
heights. After a little smoothing, Galton found that the contours
of equal frequency for this table clearly took the form of a
system of concentric ellipses. Further, when a system of vertical
lines were inserted in this diagram, he found that they each
identified a single point of maximum frequency, and that these
points of maximum frequency lay on a single straight line which
has since come to be known as a `regression line'.
These familiar results from a bivariate distribution with
elliptical contours may be regarded as a natural development of
Galton's earlier work on a system of univariate distributions.
In 1877 he had established that the frequency distribution of the
seeds produced by plants grown from sweet pea seeds of a given
size had a symmetric distribution about a particular value. This
value was smaller than the size of the parent seeds if the latter
were larger than the average for the population as a whole, and
{\it vice versa}. This is what is meant by the phrase
'regression towards the mean'.
Galton also developed a simple mechanical device for illustrating
the generation of the univariate normal distribution as a
limiting case of the binomial distribution. Lead shot is poured
in a steady stream in such a way as to fall on a particular pin
in an array of pins in the form of a {\it quincunx}, or a
lattice of equilateral triangles, on an inclined plane. Once the
shot has passed through the quincunx it is collected in a set of
rectangular compartments of equal size and the empirical
distribution examined. This device is still in existence, see
Stigler (1986, 1989).
Galton soon realised that his system of elliptical contours gave
rise to two regression lines and that these regression lines had
the same slope when the data were expressed in standard units.
In 1888 he therefore extended his analysis to define the common
slope as a measure of the 'correlation' between the chosen pair
of variables. However, Galton does not seem to have discussed the
possibility of negative values for the correlation between
variables as most of his practical examples were concerned with
the relationship between the lengths of different limbs from the
same individual.
Galton's ideas on regression and correlation were promptly taken
up and given a formal mathematical development by K. Pearson
and G.U. Yule (q.v.). At almost eighty years of age,
Galton's attention passed onto other interests. He wrote three
books on the use of fingerprints in forensic science and
investigated the operation of visual memory.
In his analyses of statistical data Galton employed the median
value and the median absolute error (or probable error) where we
would use the mean value and the root mean squared error (or
standard error). He justified his preference for median values
by analogy with a simple majority voting procedure: if there are
an odd number of electors and they all have single-humped
preference curves, then it is readily established that the value
chosen by the committee as a whole is the most preferred point
of the middlemost voter. In this context, it is interesting to
observe that Galton and Edgeworth were both champions of the
median against the mean and that they were both concerned with
the points of tangency between two mutually convex systems of
contours or indifference curves. Indeed, Edgeworth named the line
of tangency a `contract curve' in his theory of economic exchange
of 1881 and he was concerned with the intersection of two
conditional median curves in his implementation of the least
absolute deviations fitting procedure in 1887, see Farebrother
(1987).
Galton received numerous honours during his lifetime: he was
awarded honorary doctorates by the Universities of Oxford and
Cambridge in 1894 and 1895 respectively, and he was knighted by
King Edward VII in June 1909.
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\begin{thebibliography}{3}
\bibitem{1} Farebrother, R.W. (1987). The theory of
committee decisions and the double median method,
{\it Computational Statistics and Data Analysis} {\bf 5}, 437-442.
\bibitem{2} Forrest, D.W. (1974). \textit{Francis Galton:
The Life and Works of a Victorian Genius}, Paul Elek, London.
\bibitem{3} McKenzie, D.A. (1981). \textit{Statistics in
Britain 1865-1930}, Edinburgh University Press, Edinburgh.
\bibitem{4} Pearson, K. (1914-30). \textit{The Life,
Letters and Labours of Francis Galton}, Three Volumes, Cambridge
University Press, Cambridge.
\bibitem{5} Stigler, S.M. (1986). \textit{The History of
Statistics: The Measurement of Uncertainty before 1900},
Harvard University Press, Cambridge, Massachusetts.
\bibitem{6} Stigler, S.M. (1989). Francis Galton's
account of the invention of correlation, \textit{Statistical
Science} {\bf 4}, 73-86.
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\hfill{R.W. Farebrother}
\end{thebibliography}
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