99.53% and the history of probability

Abstract

What will historians make of our attempts to solve today’s medical crises? Will they be impressed by our skill at co-designing healthcare?¹ Will they shake their heads at our struggles to be inclusive towards colleagues with disabilities?² Will they wonder how we failed so miserably to teach health education in schools?³ Perhaps they will conclude, as Tom Treasure does, that although doctors should leave history to historians they should develop an interest in it?⁴

By understanding history we might have better predicted the prospects of covid-19 strategies that promoted herd immunity.⁵ We might also realise that pioneering work of one era can be discredited in another, as has happened to the research of Hans Eysenck.⁶

History also has much to teach us about fair tests and research methods, as each contribution from the James Lind Library reminds us. This month we launch a three part series on the remarkable career of Carl Liebermeister, a professor of internal medicine in the late 19th century and somebody few people will have heard of.⁷

Original research by Leonhard Held and Robert Matthews reveals Liebermeister’s role in the early debates on probability. One question that vexed the great minds of the time was to determine the level of probability at which chance could be eliminated. Simeon-Denis Poisson had proposed a p value of 99.53%, an arbitrary value that was also adopted by Jules Gavarret.

Such a stringent p value established the idea that a very large number of observations were required to answer any research question satisfactorily. But Liebermeister sensibly argued that even small studies might produce a convincing effect size. He backed up his radical thinking by developing a statistical method of demonstrating a genuine effect from any size of study, in doing so Liebermeister preceded Fisher’s Exact Test by 50 years.

The question then isn’t whether doctors should leave history to the historians, the value is clear, but whether doctors, politicians, and other policy makers are willing to look back for the answers to the future.

References

Harrison R, Ni She E and Debono D. Implementing and evaluating co-designed change in health. J R Soc Med 2022; 115: 48–51.

Ellis R, Cleland J, Scrimgeour DSG, Lee AJ and Brennan PA. The impact of disability on performance in a high-stakes postgraduate surgical examination: a retrospective cohort study. J R Soc Med 2022; 115: 58–68.

Lowry C, Rees J, Gregson D, et al. The poor relation: health education in English schools. J R Soc Med 2022; 115: 52–57.

Treasure T. Should doctors leave the history of medicine to historians? J R Soc Med 2022; 115: 73–75.

Ashton J. COVID-19 and herd immunity. J R Soc Med 2022; 115: 76–77.

Expression of concern: Articles by Hans J. Eysenck. J R Soc Med 2022; 115: 78.

Held L and Matthews RAJ. Carl Liebermeister and the emergence of modern medical statistics, part 1: his remarkable work in historical context. J R Soc Med 2022; 115: 69–72.