The last of Galton’s many contributions we will consider is his notion of correlation, which has become one of psychology’s most widely used statistical methods. In 1888 Galton published an article titled “Co-Relations and Their Measurement, Chiefly from Anthropometric Data,” and in 1889 he published a book titled Natural Inheritance. Both works describe the concepts of correlation and regression. Galton (1888) defined co-relation, or correlation, as follows:
Two variable organs are said to be co-related when the variation on one is accompanied on the average by more or less variation of the other, and in the same direction. Thus the length of the arm is said to be co-related with that of the leg, because a person with a long arm has usually a long leg, and conversely.
In a definition of correlation, the word tend is very important. Even in the above quotation, Galton said that those with long arms usually have long legs. After planting peas of varying sizes and measuring the size of their offspring, Galton observed that very large peas tended to have offspring not quite as large as they were and that very small peas tended to have offspring not quite as small as themselves. He called this phenomenon regression toward the mean, something he also found when he correlated heights of children with heights of their parents. In fact, Galton found regression whenever he cor- related inherited characteristics. Earlier, Galton had observed that eminent individuals only tended to have eminent offspring.
By visually displaying his correlational data in the form of scatterplots, Galton found that he could visually determine the strength of a relation- ship. It was Karl Pearson (1857–1936) who devised a formula that produced a mathematical expression of the strength of a relationship. Pearson’s formula produces the now familiar coefficient of correlation (r).