“Describing our whole experience”: The statistical philosophies of W. F. R. Weldon and Karl Pearson

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Abstract

There are two motivations commonly ascribed to historical actors for taking up statistics: to reduce complicated data to a mean value (e.g., Quetelet), and to take account of diversity (e.g., Galton). Different motivations will, it is assumed, lead to different methodological decisions in the practice of the statistical sciences. Karl Pearson and W. F. R. Weldon are generally seen as following directly in Galton’s footsteps. I argue for two related theses in light of this standard interpretation, based on a reading of several sources in which Weldon, independently of Pearson, reflects on his own motivations. First, while Pearson does approach statistics from this “Galtonian” perspective, he is, consistent with his positivist philosophy of science, utilizing statistics to simplify the highly variable data of biology. Weldon, on the other hand, is brought to statistics by a rich empiricism and a desire to preserve the diversity of biological data. Secondly, we have here a counterexample to the claim that divergence in motivation will lead to a corresponding separation in methodology. Pearson and Weldon, despite embracing biometry for different reasons, settled on precisely the same set of statistical tools for the investigation of evolution.

Highlights

► I examine the motivations that Weldon and Pearson had for engaging in statistics. ► It is often argued that reasons for using statistics lead to different methods. ► Weldon and Pearson, however, have different motivation but identical methods. ► Weldon’s philosophy of science is interesting, yet under-studied.

Section snippets

Pearson and statistics

In addition to being a pioneer in statistics, Pearson was a profound philosopher of science in his own right, and was intensely reflective about his methodology and motivations. His philosophy of the physical sciences in particular, as expressed in his completion of W. K. Clifford’s Common Sense of the Exact Sciences and his own Grammar of Science, was extensively developed, and, while formulated independently from the views of Ernst Mach (with whom Pearson corresponded only late in his career),

Weldon and the Nature debate

On the traditional reading of the relationship between Pearson and Weldon, we would expect the two men to view statistics in precisely the same way. As the story usually goes, Weldon is the empirically-minded biologist who approaches Pearson when he feels his experimental problems might be helped by statistical methods. Beyond this point, Pearson and Weldon are deemed to be all but philosophically, methodologically, and motivationally identical.

Weldon on statistics

In 1906, the year of his death, Weldon contributed a piece on “Inheritance in Animals and Plants” to a collection of lectures on scientific method (Weldon, 1906). Its breadth and central concerns are quite exciting—Weldon offers a sustained defense of the use of statistical methods in science, both generally and with particular emphasis on the biological sciences.

Why would statistical methods require a defense? According to Weldon, they inherently require a compromise—a methodological value

Conclusions

With a novel conception of Weldon’s philosophy of science in hand, we can turn to reevaluating the relationship between Pearson and Weldon. While their overall methodologies were all but identical, as were their ideas of valuable data and good experimental process, this agreement masks the fact that their motivations for engaging in statistics were interestingly divergent. Pearson, I have argued, views statistics as a tool for positivist simplification, while Weldon sees it as essential for the

Acknowledgments

Many thanks are due to Phil Sloan for tireless and extensive comments on this paper throughout its production, and to Tom Stapleford for invaluable help with broader connections to the history of statistics. Thanks to Theodore Porter for comments on Pearson. I’ve also had several very useful exchanges with Gregory Radick on the topic of W. F. R. Weldon. Thanks as well to several anonymous referees for comments on earlier versions. Finally, this paper also benefitted from audiences at ISHPSSB

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