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The Introduction of Mathematical into Medical Research: The Roles of Karl Pearson, and

Eileen Magnello

I look upon statistics as the handmaid of medicine, but on that very account I hold that it befits medicine to treat her handmaid with proper respect, and not to prostitute her services for controversial or personal purposes. 1

Karl Pearson

This chapter will examine Karl Pearson’s role in the medical community and, in particular, the promulgation of his statistical methods by his students including Major Greenwood, John Brownlee and Austin Bradford Hill. Their collective efforts led to the successful adoption of in medicine and thereby transformed medical research in the twentieth century. The value of mathematical statistics to medical research, they maintained, was that it provided a set of rigorous tools for workers in clinical or preventive medicine who were often unable to conduct experiments or who had to work with records already available (unlike the laboratory worker who had an already existing set of tools). Medical practitioners argued that statistical methods could provide ‘clearer insight into the phenomenon of epidemic disease’, measure the statistical accuracy of various instruments, give a ‘rational prognosis’ and ‘secure a logical basis’ for medical research. 2 In short, research undertaken would be more reliable and the results would afford greater confidence when appropriate statistical methods were utilised. Whilst applications of some types of statistics to problems of had been made by Adolphe Quetelet, and W.F.R. Weldon by the end of the nineteenth century, P earson ultimately created a new discipline of mathematical statistics. He did this when he established the Biometric School in 1893 (and later the

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Drapers’ Biometric Laboratory in 1903), founded the journal Biometrika with Weldon and Galton in 1900 and set up the first degree course in statistics in Britain in 1917. Prior to Pearson establishing this new discipline, the General Register’s Office had been the centre for the collection and tabulation of medical statistics. The principal form of statistics used throughout much of Victorian Britain was, in , vital statistics and actuarial methods. This use and type of statistics began to change in the 1870s when Francis Galton began to examine statistical and biological variation and showed that standardised comparisons could be made by using the law of frequency (or the ). At the end of the nineteenth century, the content and practice of statistics underwent a series of transitions that led to its emergence as a highly specialised mathematical discipline. These intellectual (and later institutional) changes were, in part, brought about by a mathematical-statistical translation of the Darwinian change in ideas about what kinds of natural processes occur in the world. The Darwinian idea that had the greatest impact on the development of mathematical statistics, was Darwin ’s redefinition of the biological species as something which could be viewed in terms of populations; in contrast, the Aristotelian essentialistic idea of ‘ types’, which formed the basis of the morphological or typological concept of species used by a number of biologists until the end of the 19th century, focused on averages rather than on individual variation. Pearson’s and Weldon’s mathematica l reconceptua lisation of Darwinian ‘statistical’ populations of species in the 1890s, thus provided the framework within which a major paradigmatic shift occurred in statistical techniques and theory. 3 This view is, however, in contrast to much of the scholarship on the origins of Pearsonian statistics. Most historians have argued that Pearson’s interests in provided the impetus to the development of his statistics. 4 This argument has, however, not only overlooked Pearson’s earliest statistical work, but it has also neglected the totality and complexity of the full range of the various quantitative and statistical methods that Pearson devised and deployed in all four of his laboratories. 5

Vital statistics Hence, two different statistical methodologies were created in the nineteenth century which differed ideologically, conceptually and mathematically and these distinctions may be seen in Figure 5.1. Vital statistics, which is undoubtedly the way in which the word ‘statistics’ is most commonly understood, is used as a plural noun as 96