Manipulation and Population Statistics in Nineteenth-Century France and England

Social Research, Summer, 2001 by Libby Schweber

For each debate I will ask: What are the different considerations at play in the discussion? How are they related? Are technical considerations addressed separately from other interests or is one a proxy for the other? And, finally, what elements do the traces left by these controversies provide to help explain differences in the dynamic of the French and British cases?

MacKenzie: The Debate over Correlation Coefficients

MacKenzie's 1978 article, "Statistical Theory and Social Interests: A Case Study," was one of the founding studies of the interest approach in the social studies of science (or "strong program" as it was originally called). The article discussed the debate between Karl Pearson and George Udny Yule over the choice of a measure of correlation for nominal (rather than interval) variables. While measures of correlation had already been developed for continuous variables, they had not yet been applied to the correlation between discontinuous variables.

In the space of a year both Pearson and Yule proposed a solution to this problem. The main difference between their proposals stemmed from the mathematical properties they built into the index. Yule's measure established the fact of association on the basis of simple mathematical properties (complete association if Q = 1, negative association if Q = -1, and independence if Q = 0). Pearson's coefficient, in contrast, measured the strength of association. He achieved this by working with the ungrounded hypothesis that observed values corresponded to an underlying bivariate normal distribution. This assumption allowed him to build on the mathematical properties of the normal distribution. In 1900 both men published their "invention." The controversy was played out between 1900 and 1914 in the Journal of the Royal Society and in Biometrika, the scientific journal associated with the eugenics movement

On a purely technical level, both measures were mathematically reasonable and both continue to be used today. The question MacKenzie raises is how to explain why each person clung to his position. In the article he argues that differences between Yule's and Pearson's commitment to their respective measures were associated with differences in what MacKenzie describes as "cognitive interests." MacKenzie uses the term "cognitive interests" to refer to "those aspects of the actual or potential scientific applications of theories which `feed back' into theoretical development by structuring scientists' construction and judgment of theories" (1978: 48). "Cognitive interests" thus refers to those practical applications that directly influence theoretical developments.

Both Pearson and Yule explicitly intended their measure to be used as a practical tool for testing hypotheses concerning the relation between statistical entities. They differed, however, in the nature of these interests. Pearson's cognitive interests were related to existing achievements in mathematical statistics, notably interval-level theory of correlation and regression. His new measure rested on an analogy between interval-level data and nominal variables. In contrast, Yule developed an approach that accepted the limits of nominal data and thus only allowed for very general forms of prediction.