Co-relations and their measurement, chiefly from anthropometric data in Proceedings of the Royal Society of London 45, 1888, pp. 135–145 [GALTON'S CORRELATION COEFFICIENT]. Francis Galton.

Co-relations and their measurement, chiefly from anthropometric data in Proceedings of the Royal Society of London 45, 1888, pp. 135–145 [GALTON'S CORRELATION COEFFICIENT]

London: Royal Society, 1888. 1st Edition. FULL VOLUME: 1st EDITION OF FRANCIS GALTON’S INVENTION, DEVELOPMENT, & DEMONSTRATION OF WHAT WOULD BECOME KNOWN AS THE CORRELATION COEFFICIENT (the statistical concept of correlation or, at publication, ‘Co-relation’). “Contemporary scientists often take the correlation coefficient for granted [so don’t] appreciate that before Galton…the only means to establish a relationship between variables was to deduce a causative connection. There was no way to discuss, let alone measure, the association between variables that lack a cause-effect relationship” (Samuel, Correlation and Dependence, 26).

Francis Galton’s pioneering work in statistics began with his study of heredity. In 1884, Galton, a cousin of Charles Darwin, founded the Anthropometric Laboratory, there gathering data on the physical measurements of people. He began to notice correlations. After Galton “collected [a] vast array of data from thousands of individuals, [he was then] confronted by a host of methodological problems never before encountered by researchers” (Blocher, The Evolution, 38).

To make meaning of the data, Galton drew “on the work of the Belgian mathematician Adolph Quetelet, one of the first to apply mathematical models to frequency distributions of human characteristics” (ibid). “Quetelet was struck by the fact that a plot of variation in the frequency of height around a population mean gave a result that conformed exactly to the bell-shaped curve predicted by the Gaussian law of errors. In other words, the variation of a particular anthropometric characteristic [say, height] in a population of individuals is distributed in precisely the same way as the measurement errors made by astronomers that Gauss analyzed” (UVIC).

Inspired by the ‘laws of errors’ (now the normal curve) and thinking that it might be applicable to the study of heredity, Galton plotted points noting that his anthropometric data tended to fit [Quetelet’s] ‘normal curve’. He began to estimate the probability of occurrence of given deviations from the norm or average” (ibid).

But Galton was not simply interested in his anthropometric data. He also believed that intelligence is inherited. To prove it, Galton knew he “needed a method to show that the intelligence of one generation was "co-related" to that of the previous generation” (Brutlag). He later wrote that his challenge was that “the primary objects of the Gaussian Law of Errors were exactly opposed, in one sense, to those to which I applied them. They were to be got rid of or to be proved a just allowance for errors. But these errors or deviations were the very things I wanted to preserve and know about” (DSB, V, 266).

Finding it difficult to quantify the deviations in his data, Galton invented and then applied the statistical concept of ‘co-relation’ (later correlation), a formula to determine how strong a relationship is between data. Galton defined co-relation [in this paper] as “Two variable organs are said to be co-related when the variation of the one is accompanied on the average by more or less variation of the other, and in the same direction” (Galton 135). His definition also reveals the properties of his correlation coefficient: “a measure of strength of a linear relationship; the closer it is to 1, the closer two variables can be predicted from one another by a linear equation” (Brutlage).

Importantly, this paper also demonstrates Galton’s discovery of “the phenomenon of regression to the mean [“the tendency of offspring to show less of a given characteristic than an extreme amount evident in a parent”] and he is responsible for the choice of r (for reversion or regression) to represent the correlation coefficient” (ibid.; Clauser, JEBS 2007, 440). Item #542

CONDITION: Complete. 8vo. Two title page stamps, a few within, no exterior markings. Handsomely rebound in calf over aged marbled paper boards; 5 raised bands at the spine; gilt-lettered & tooled. Marbled text block & 10 plates. Near fine.

Price: $575.00