Victorian vital and mathematical statistics

Abstract

Medical practitioners were largely responsible for the development and application of vital statistics in the mid-nineteenth century, whilst mathematicians established the discipline of mathematical statistics at the end of the nineteenth century in Victorian Britain. The ground-breaking work of such vital statisticians as T R Malthus, William Farr, Edwin Chadwick and Florence Nightingale are examined. Charles Darwin's emphasis of individual biological continuous variation, which played a pivotal role in the epistemic transition from vital to mathematical is assessed in the context of the innovative work of these mathematical statisticians: Francis Galton, W F R Weldon, and primarily Karl Pearson with contributions from Francis Ysidro Edgeworth, George Udny Yule and William Sealy Gosset.

Notes

1 The first comprehensive census was not undertaken in England until 1851 when provisions were made to include age, sex, occupation and birthplace, as well as counting the blind and the deaf.

2 It was largely Chadwick's work that led to the first Sanitary Commission in 1838. Chadwick followed this work with his Inquiry into the Sanitary Conditions of the Labouring Population of Great Britain in 1842.

3 By the middle of the nineteenth century, vital statistics had become an important feature of mid-Victorian preventive medicine and public hygiene, and continued to play a pivotal role for medical practitioners throughout the period.

4 This was the sobriquet given to her in 1913 by her first biographer, Sir Edward Cook.

5 Nightingale found that whilst 20 per 1000 died in military hospitals, 10 per 1000 died in civil life.

6 For example, hospital statistics gave very little useful information on the average duration of hospital treatment or on the proportion of patients who recovered, compared with those who died.

7 The results of these hospital reports were printed in the Journal of the Statistical Society in 1862. Though the forms were used for a period of time, eventually, the hospitals found them too costly and too time consuming to administer.

8 By 1891 Oxford University appointed the distinguished statistician, Francis Ysidro Edgeworth (1845–1926) to the Chair of Political Economy at All Soul's College.

9 See Pearson (1924, 21). More than a century would pass before Oxford renamed their Department of Biomathematics as the Department of Applied Statistics in 1988.

10 Whilst Galton endorsed the vital-statisticians' idea that statistics could be used to enumerate social conditions, he differed from this group because he was also interested in measuring biological variation.

11 To answer these questions, he decided to experiment with sweet pea seeds in 1875, which his cousin Charles Darwin and the botanist Joseph Hooker had recommended using, since sweet peas were a sturdy and prolific plant whose seeds were the same size. Galton then began to measure the diameter and the weight of thousands of mother and daughter sweet pea seeds in 1875, which he classified into seven groups, according to their size. After measuring the diameter and the weight of thousands of mother and daughter sweet pea seeds in 1875, Galton found that the population of the offspring reverted towards the parents and followed the normal distribution. He initially termed this method “reversion”, which he expressed as the letter r.

12 Pearson had learnt about the method of moments when he was a student at Cambridge. His first paper on the this topic was published a year after he graduated (Pearson 1890).

13 Pearson learnt about the method of moments from graphical statics when determining moments on a loaded continuous beam with the help of a theorem proved in 1857 by the French engineer Emile Clapeyron.

14 This method reduces a set of complex data into a more manageable form and makes it possible to detect structures in the relationship between variables.