What students are told to do in textbooks is sometimes not what members of the discipline do in their own research, according to Peter F. Halpin and Henderikus J. Stam, two University of Calgary historians of psychology,
It has long been recognized that there are two very different interpretations of the common null-hypothesis statistical testing (NHST) procedure. One, started by NHST’s inventor, Ronald Fisher, sets forth only a null hypothesis (Ho) and interprets data that would occur only very improbably under Ho as reason to reject Ho (but not in favor of any specified alternative). The other tradition, begun by J. Neyman & E. S. Pearson, sets out two hypotheses — the null (Ho) and the alternative (H1) and interprets data that would occur improbably under one (e.g., Ho) as reason to “accept” the other (e.g., H1). Neyman and Pearson also developed an elaborate theory of the failure to reject the null when it is not true (“Type II error”) and the related “power” of statistical tests. In 1987 Gerd Gigerenzer & David Murray noted that what was typically taught in statistical textbooks was neither of these systems of interpretation, but rather an incoherent “hybrid” of the two that neither party would have accepted.
Halpin and Stam, whose article appeared in the Winter 2006 issue of American Journal of Psychology, show that although Gigerenzer and Murray were correct that textbooks published between 1940 and 1960 taught the “hybrid” interpretation of statistical tests, this trend did not extend into the published research literature of the era. There, the Fisherian interpretation reigns supreme, and one rarely finds the terminology characteristic of the Newyman-Pearson interpretation.
The article is entitled, “Inductive inference or inductive behavior: Fisher and Neyman–Pearson approaches to statistical testing in psychological research (1940–1960).” It is available to on-line to subscribers only, but the abstract can be found on PubMed.