Statistics on the Table: The History of Statistical Concepts and Methods (review)

Statistics on the Table: The History of Statistical Concepts and Methods. By Stephen M. Stigler. Cambridge: Harvard Univ. Press, 1999. Pp. 488. $45.

I was not able to find a definition or a characterization of the discipline of statistics in the recently published Cambridge Dictionary of Statistics (Everitt 1998). However, I did find the following definition from the third edition of A Dictionary of Epidemiology (Last and Abramson 1995): "The science and art of collecting, summarizing, and analyzing data that are subject to random variation." The fact that this discipline can be characterized as an "art" as well as a "science" has made for a lively and controversial history, and the flavor of this history is well captured in the second major book on the history of statistics by Stephen M. Stigler. In this volume, he presents a series of 22 essays on the historical development of some major statistical concepts and issues. Except for a relatively brief digression into the 17th century, the time period covered by these essays is mostly mid-to-late 19th century, with occasional "jumps" into the 20th century. Stigler's earlier (1986) volume on the history of statistics covered primarily the 17th through 19th centuries.

The title of the book, Statistics on the Table, is based upon a challenge issued by Karl Pearson in a 1910 letter to the London Times (described in the first chapter). This letter was motivated by a major dispute between Pearson and several Cambridge economists--including Alfred Marshall, John Maynard Keynes, and Arthur Pigou--over conclusions reached by the authors of a cross-sectional study that attempted to estimate the health effects on children of their parents' consumption of alcoholic beverages. Pearson evidently had considerable input in that study and in the expression of its conclusions, which essentially found little or no relationship between alcoholic beverage consumption in the parents and certain physical or mental characteristics, such as height and intelligence, in their children. The publication of this finding resulted in a wave of criticism on the part of the Cambridge economists mentioned above. Pearson, in turn, felt that this criticism was based on suggestion and unproven conjecture, and challenged his critics with the reply:

Statistics--and unselected statistics--on the table, please. I am too familiar with the manner in which actual data are met with the suggestion that other data, if they were collected, might show something else to believe it to have any value as an argument. "Statistics on the table, please," can be my sole reply.

In his retelling of this controversy (now, nearly a century old), Stigler indicates "the issues behind Pearson's battle with the Cambridge economists remain significant conceptual hurdles in quantitative social science today" (p. 5). Indeed, in spite of the amazing advances over the past 100 years in the statistical sciences, the tone and substance of this controversy sounds much like those that we encounter every day in scholarly journals as well as the mass media (e.g., the extent and impact of the undercount in the U.S. Census, or the health effects of exposure to environmental tobacco smoke or electromagnetic fields). Stigler's detailed account of this controversy highlights the skill and creativity that Pearson and his adversaries employed in identifying and characterizing threats to the internal and external validity of conclusions made from observational studies. While these various sources of error have been categorized, named, and disseminated widely to the scientific world since their time, the concepts and ideas were certainly known and used by Pearson and his contemporaries.

The 22 essays in this book are grouped into five general sections. The first section, "Statistics and Social Science," describes forays into quantitative studies in the social sciences by 19th-century economists and statisticians, including Adolphe Quetelet (conception of the "average man"), William Stanley Jevons (use of index numbers), and Francis Ysidro Edgeworth (overall statistical contributions...