Francis Galton as Statistician

Galton was able to place his researches about heredity on a scientific basis by applying novel statistical concepts, and can justly be claimed as one of the very first social scientists, if not the first. This would pave the way for the development of statistics as a discipline, through Galton's follower Karl Pearson. It would also lay the foundation for the study of differential psychology: through Charles Spearman, who was heavily influenced by Galton and made important contributions of his own to the development of factor analysis; and through Cyril Burt and his pupils, who moulded the study of intelligence and hereditary ability into a formidable discipline. There are few aspects of modern social science that do not (or at least, should not) rely on the statistical innovations that Galton introduced.

Ironically, Galton was not himself a mathematician, though he was competent enough, but really an intensely practical man. He left the refinement of his techniques to dedicated and supremely talented mathematicians like Pearson, but provided the crucial formation of concepts; he was a practical innovator, not a technician. Galton first discovered regression, which he initially called reversion, by experimenting with sweet peas. His sweet peas produced seeds with a (normal) variation of sizes that regressed from the distribution of their parents. 

Some years later,  he formulated the statistical correlation coefficient by another indirect route, painstakingly graphing and re-graphing his data about bivariate normal distributions until he realized that the formulae for elliptical curves (a topic popular in 19th century mathematics but almost entirely moribund today) could provide him with a method for summarizing with a number the graphical relationship he saw.  This number could then be used to reason about the relationship, and form a basis for comparisons. Following the suggestion of a friend, he approached a Cambridge mathematician to work out the details for him - an approach he was able to pursue very fruitfully in later years with Pearson.

Facsimile 1874 On a proposed statistical scale. [Letter] Nature 9 (March 5) : 342-3
Facsimile 1875 'Statistics by intercomparison with remarks on the Law of Frequency of Error.' Philosophical Magazine 49 : 33--46
Facsimile 1877 'Considerations adverse to the maintenance of Section F.' Journal of the Statistical Society 40 (September) : 468-73
Facsimile 1879 'The geometric mean, in vital and social statistics.' Proceedings of the Royal Society 29 (November 20) : 365-7
Facsimile 1885 'Anthropometric percentiles.' Nature 31 : 223-5
Facsimile 1888 'Co-relations and their measurement, chiefly from anthropometric data.' Proceedings of the Royal Society 45 (December 13) : 135-45
Facsimile 1889 'Correlations and their measurement, chiefly from anthropometric data.' Nature 39 : 238
Facsimile 1890 'Kinship and Correlation' North American Review 150 : 419-431
Facsimile 1890 'Dice for statistical experiments.' Nature 42 : 13-4
Facsimile 1892 Notes to George K. Holmes on the Subject of Distribution Publications of the American Statistical Association : 271-3
Facsimile 1894 'Note on fitting normal curves to distribution of speeds of old homing pigeons' Homing News and Pigeon Fanciers' Journal (April 6) : 159-60
Facsimile 1894 'A plausible paradox in chances.' Nature 49 : 365-6
Facsimile 1895 'A new step in statistical science.' [Letter] Nature 51 : 319
Facsimile 1896 "Application of the Method of Percentiles to Mr. Yule's Data from the Distribution of Pauperism". Journal of the Royal Statistical Society 59 : 392-396
Facsimile 1897 'Note to the memoir by Professor Karl Pearson, F.R.S., on spurious correlation.' Proceedings of the Royal Society 60 (February 18) : 498-502
Facsimile 1899 'The median estimate.' Report of the British Association for the Advancement of Science 69 : 638-40
Facsimile 1899 'The median estimate.' Nature 60 : 584
Facsimile 1899 'A geometric determination of the median value of a system of normal variants from two of its centiles.' Nature 61 : 102-4
Facsimile 1902 'The most suitable proportion between the values of first and second prizes.' Biometrika 1 : 380-90
Facsimile 1907 'Grades and deviates.' Biometrika 5 : 400-4

Galton has left an excellent description of his discovery of correlation and regression, in an article he published for the North American Review in 1890, "Kinship and Correlation".  Some idea of Galton's influence on statistics can also be gained from the following obituary, which appeared in the Journal of the Royal Statistical Society.