The History of Statistics: The Measurement of Uncertainty Before 1900. - book reviews

Monthly Labor Review, May, 1989 by Dave McDermott

The History of Statistics: The Measurement of Uncertainty Before 1900.

In 1823, Pierre Simon LaPlace, French mathematician, succinctly stated the challenge of statistics with his call for:

...a method for determining the probability that the

error in the obtained results is contained in narrow

limits, a method without which one risks presenting

the effects of irregular causes as laws of nature... Stephen Stigler's book is a rigorous history of the development of statistical tools which attempt to meet LaPlace's challenge.

Stigler directs his history of statistics at the evolution of techniques for quantifying the uncertainty of measurements. His choice is significant. By defining the pertinent topic to be the measurement of uncertainty, he concentrates on the tools which make modern statistics powerful. The skill which separates statistics from blind number-crunching is the statistician's ability to quantify the certainty of the measurements he or she produces.

Stigler takes on a formidable task. Since the 18th century, statistical nomenclature has changed to such an extent that it is difficult to discern the arguments of the early statisticians. The challenge is compounded by the fact that none of the key players in the development of statistics thought of themselves as statisticians. Statistics as a separate discipline did not exist prior to about 1900. Much of the statistical work of the 18th and 19th centuries was done as an adjunct to physical science. Researchers tended to put more effort into the clarity of their principal arguments and considerable less into the clarity of their statistical expositions.

Stigler successfully extracts the essential statistical developments out of 200 years of physical and social science. He then attempts to gauge how well scientists of the 18th and 19th centuries anticipated the direction and significance of their statistical work.

The result is a remarkably clear picture of the development of the discipline. In the mid-1700's, scientists debated whether techniques for combining observations were legitimate. Even combining several different observer's measurements of the same object was challenged by mathematicians as illustrious as Leonhard Euler on the grounds that true values would be corrupted by erroneous ones. It was not until the concept of random errors was developed in the mid-1700's that it became defensible to combine observations with the expectation that random errors would tend to cancel each other rather than reinforce each other.

History of this sort is humbling for practitioners in the field of statistics. It illustrates how new and untested our discipline is. Some of the arguments which nonstatisticians level at the discipline today have their roots in the debates which Stigler documents. In the early 1800's, LaPlace and Adolphe Quetelet argued vigorously for estimating population in France and Belgium by means of sample surveys. The Baron de Keverberg, a Belgian official, criticized this radical idea. Keverberg argued that only a survey which had as many sampling units as there were residents could be counted on to accurately represent the varying birth and death rates of different provinces. Keverberg's argument, which won over Quetelet, is strikingly similar to the complaints of those who argue that national statistical series fail to take into consideration the peculiarities of their region, no matter how subtle the sampling may have been. Stigler does the statistical community a service by reminding us that criticisms of this sort, which are often dismissed as naive, have an honorable intellectual heritage.

The history is also a valuable insight into the process of scientific revolution. In a short 200 years, an entire discipline was born and refined. Historians of science will appreciate the effort Stigler makes to document the dynamics of the development of essential concepts of contemporary statistics, complete with the false starts, clashes of personality, vituperative exchanges, and obstructionism which impede all scientific revolutions.

While the book is a fine history, it is not written for a general audience. Stigler makes no effort to insulate the reader from exact mathematical reasoning. The book can only be appreciated if one is willing to follow his mathematical as well as his prose arguments.