History

I suggest that the most useful history of statistics would start with our predecessors’ conceptions of the purposes of statistics. Such a “goal-orientation” helps explain why these thinkers developed the techniques they did. R.A. Fisher (“Statistical Methods for Research Workers,” 1925), commonly regarded as the father of modern statistics, and J.O. Berger (“Statistical Decision Theory,” 1985) portray the discipline of statistics as a collection of methods for addressing—based on data—two universal human needs: to know, and to do. To these needs correspond two branches of statistics: Statistical Inference and Statistical Decision Analysis. The former is the business of making statements about the probability, credibility or plausibility of scientific hypotheses. The latter tries to identify the likely or expected consequences of various decisions, which in turn are defined as allocations of resources.

R. Royall (“On the Probability of Misleading Statistical Evidence,” JASA, 2000, author’s rejoinder), representing a so-called “Evidentialist” paradigm, identifies yet another role of statistics: To measure the “evidence” conveyed by a set of data x in favor of one hypothesis, H0, vis-à-vis another, H1. We may view this form of evidence as the degree to which the odds Pr(H0)/Pr(H1) change to Pr(H0|x)/Pr(H1|x) due to observing x (here, the “|x” notation is read “given x”).

Royall illustrates these three strands of statistics using a medical diagnostic test designed to detect the presence of a particular disease. He portrays a physician who, using one of his patient’s test results, seeks to answer the following three questions:

• Should the data lead me to believe the patient has the disease?
• Does the data justify my acting as if the patient has the disease?
• What do the data say?

These questions correspond, directly and respectively, to Statistical Inference, Decision Theory and Evidential Analysis.