Statistics

# Karl Pearson on why the idea of the correlation coefficient, not the formula, was the real breakthrough

The idea of correlation (i.e., mutual influence/intimate connection), indeed even the word correlation, existed for centuries before Francis Galton. Galton’s (1888) revolutionary idea was not that correlation exists but that it can be quantified. The correlation coefficient most often used today bears the name of statistician Karl Pearson, Galton’s friend and biographer. Though Pearson refined Galton’s formulas, providing them with a lasting and secure mathematical foundation, Pearson (1930) was quite clear that it was the idea of the correlation coefficient, not the formula, that was the real breakthrough:

Up to 1889 men of science had thought only in terms of causation, in future they were to admit another working category, that of correlation, and thus open to quantitative analysis wide fields of medical, psychological and sociological research. Turning to the writings of Turgot and Condorcet, who felt convinced that mathematics were applicable to social phenomena, we realize to-day how little progress in that direction was possible because they lacked the key—correlation—to the treasure chamber. Condorcet often and Laplace occasionally failed because this idea of correlation was not in their minds. Much of Quetelet’s work and that of the earlier (and many of the modern) anthropologists is sterile for like reasons.

Galton turning over two different problems in his mind reached the conception of correlation: A is not the sole cause of B, but it contributes to the production of B; there may be other, many or few, causes, some of which we do not know and may never know. Are we then to exclude from mathematical analysis all such cases of incomplete causation? Galton’s answer was: “No, we must endeavor to find a quantitative measure of this degree of partial causation.” This measure of partial causation was the germ of the broad category—that of correlation, which was to replace not only in the minds of many of us the old category of causation, but deeply to influence our outlook on the universe. (pp. 1–2)

## References

Galton, F. (1888). Co-relations and their measurement, chiefly from anthropometric data. Proceedings of the Royal Society of London, 45, 135–145.

Pearson, K. (1930). The life letters and labours of Francis Galton: Volume III. Researches of middle life. Cambridge, England: Cambridge University Press.

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