London: Royal Society, 1888. 1st Edition. FIRST EDITION OF FRANCIS GALTON’S DEVELOPMENT AND DEMONSTRATION OF WHAT WOULD BECOME KNOWN AS THE CORRELATION COEFFICIENT. After examining correlations in forearm and height measurements and noticing “a common thread in three different scientific problems he was studying”, Galton “demonstrated its application in the study of heredity, anthropology, and psychology” (Project Euclid; Wikipedia).
Galton was a cousin of Charles Darwin’s, and in 1884 he founded the Anthropometric Laboratory, there gathering data through the physical measurement of hundreds of people. “Galton however, was not merely interested in physical characteristics, as he claimed that intelligence is inherited. To demonstrate this, he needed a method to show the intelligence of one generation was "co-related" to that of the previous generation, so that he might argue for the causal relationship: children acquired intelligence from their parents. Fortunately, Galton understood that the scientific value of such a method required it be developed apart from the study of human mental characteristics, which were difficult to quantify in numerical measurements.
He developed the ideas of correlation and regression in the study of sweet peas and human physical characteristics. Three papers presented these new concepts and their first methods of calculation: "Regression towards mediocrity in hereditary stature" (1885), "Family likeness in stature" (1886), and "Co-relations and their measurement, chiefly from anthropometric data." [this paper]…
In this work, Galton defines correlation: '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.... It is easy to see that co-relation must be the consequence of the variations of the two organs being partly due to common causes... If they were in no respect due to common causes, the co-relation would be nil' (Galton, “Co-relations”, 135).
Galton's definition reveals the properties of the correlation coefficient. It is 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. It is a measure of direction: a positive correlation indicates X, Y increase together; a negative correlation indicates one decreases as the other increases. Note that Galton does not claim that co-relation implies cause-effect (it would be absurd for one to assume the size of one organ determined the size of another) (Brutlag, The Development of Correlation and Association in Statistics, 2007). Item #542
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