The Rise of Statistical Thinking, 1820-1900 Reprint Edition

Stephen Stigler has been a master at researching and writing about statistical ideas and research from the 19th and 20th Centuries. In this book Porter lives up to the standards of Stigler and presents us with a well written historical account of the mathematicians, probabilists and statisticians who developed the ideas in the 19th Century that led to the explosion of the use of statistical methods in the 20th Century.

If you like the history of statistics and have read Stigler you will like Porter also. If you like Porter you should also look at "The History of Statistics: The Measurement of Uncertainty Before 1900" and "Statistics on the Table: The History of Statistical Concepts and Methods" both by Stephen Stigler. David Salsburg's "The Lady Tasting Tea" is a recent tribute to the developments of statistics in the 20th Century and the men and women that made it all possible. It is a fitting sequel to this book of Porter's.

What is the impact of regular excercise or smoking on the chance of having a heart attack? Is the difference between the average income of the top ten percent and the bottom ten percent of Americans widening? Topics like these are staples of news articles every day, but they were only made possible by a revolution in thought that occurred during the nineteenth century--the rise in statistical thinking--that Porter's book recounts.
The story of the introduction of the scientific method in the 17th century is familiar. The discovery of the laws of probability by Pascal--prompted by a friend's interest in solving a gambling problem--has also been presented in several books. But the habit of thinking numerically about populations only arose in the 19th century, and this story is less well known.
It was during the 19th century that it became common to examine the characterists of populations, for example, the average number of suicides, deaths, or crimes each year. The mathematical concepts that are now taught to most high school and college students--mean, median, the normal distribution or bell curve, and correlation--were developed by the end of the century.
By stressing the broader intellectual context of these developments, Porter highlights some interesting perspectives. For example, statistics was the province of reformers who believed that government neither could, nor should, do much to change society. Also, I hadn't realized the importance of Darwin's theory--and its bastard child, eugenics--as a motivation to so many statisticians.
Statistical concepts were developed by social scientists, and only later adopted by physical scientists. This reverses the more common 'physics' envy, where social scientists see the physical sciences as the gold standard and attempt to copy their methods.
Although his topic is fascinating, Porter's book is not, at least for the nonspecialist. Porter's academic prose rarely made the subject come alive, and I found myself soldiering on and waiting eagerly for the last page.
One problem was that Porter never explains any of the concepts he discusses, assuming that the reader is familiar with them. In my case, that was fine for basic statistical concepts like standard deviation and regression, but I was lost in many other places, such as his discussion of the theory of gases.
As an alternative, Ian Hacking's book, The Taming of Chance, is a discussion of the philosophical implications of many of these developments (although it doesn't cover Galton, Edgeworth, and Pearson). I found it gripping throughout, and it is extremely well written, at least for an academic.

In “The Rise of Statistical Thinking, 1820 – 1900”, Theodore M. Porter argues, “The doctrine that order is to be found in large numbers is the leitmotif of nineteenth-century statistical thinking. The regularity of crime, suicide, and marriage when considered in the mass was invoked repeatedly to justify the application of statistical methods to problems in biology, physics, and economics” (pg. 6). He continues, “The use of probability relationships to model real variation in natural phenomena was initially made possible by the recognition of analogies between the objects of these sciences and those of social statistics” (pg. 6). Porter further argues, “The history of statistics sheds light on the relations between abstract science and what are often seen as its applications. In truth, practice was decidedly ahead of theory during the early history of statistics, and ‘pure’ or abstract statistics was the offspring, not the parent, of its applications” (pg. 10).
Porter writes, “Implicit in the use by political arithmeticians of social numbers was the belief that the wealth and strength of the state depended strongly on the number and character of its subjects” (pg. 19). Further, Porter links statistics to the rise of modern bureaucracy, writing, “The information that numbers could provide was vital for controlling the population, and especially for augmenting tax revenue. More fundamentally, however, the ideal of enumeration was one which few other than agents of the crown would seriously have entertained, at least on the Continent, under the Old Regime – and monarchs typically regarded demographic figures as a state secret, too sensitive to publish” as it might eliminate the basis of social hierarchies (pg. 25). Porter writes,
“Until the nineteenth century, then, statistical regularity was generally seen as pertaining to the natural history of man, and as indicating divine wisdom and planning. The first well-publicized instance of statistical order which could not be plausibly interpreted in this way was Laplace’s announcement in the “Philosophical Essay on Probabilities” that the number of dead letters in the Paris postal system was constant from year to year. The uniformity of murder, theft, and suicide was even more difficult to explain in natural-theological terms. Quetelet was, in some sense, able to do so, but only by embracing a cosmology at once physicalist and theological that made mass regularity the expected outcome of natural processes in every domain” (pg. 51).
While this would seem to question free will, Porter describes Buckle as working out a compromise position.
Porter writes, “The mathematics of variation was instrumental for the impressive achievements of the nineteenth-century kinetic theory, including Boltzmann’s reduction of the second law of thermodynamics to mechanics and probability theory. It also provided the key in biology to the quantitative study of heredity, leading eventually to what is now the most purely statistical of the natural sciences, quantitative genetics. Beyond its importance for particular natural and social sciences, however, the new understanding of the error law that derived from Quetelet’s work proved essential for mathematical statistics itself” (pg. 110). He continues, “The theory of evolution by natural selection provided the context in which statistical biology was introduced, and within which it has since been most fruitfully developed” (pg. 134). Porter further writes, “Statistical determinism became untenable precisely when social thinkers who used numbers became unwilling to overlook the diversity of the component individuals in society, and hence denied that regularities in the collective society could justify any particular conclusions about its members” (pg. 151). In this way, “Blind use of averages threatened to supplant that je ne sais quoi, medical tact, upon which physicians prided themselves. Accordingly, the so-called numerical method in medicine was viewed by many with suspicion, and subjected on occasion to vitriolic attacks” (pg. 157).
Finally, Porter writes, “The stimulus for a successful mathematical statistics came less from the theory of errors of observation than from the use of probability distribution formulas to model real events in nature and society. Its beginnings are to be found in the last quarter of the nineteenth century, partly in Germany, where probabilistic analysis was first applied constructively to statistical social science between 1875 and 1880, but primarily in Great Britain” (pg. 232).