Summary The attempt to reinterpret the common tests of significance used in scientific research as though they constituted some kind of acceptance procedure and led to “decisions” in Wald’s sense, originated in several misapprehensions and has led, apparently, to several more. The three phrases examined here, with a view to elucidating the fallacies they embody, are: (i)“Repeated sampling from the same population”,(ii)Errors of the “second kind”,(iii)“Inductive behaviour”. Mathematicians without personal contact with the Natural Sciences have often been misled by such phrases. The errors to which they lead are not always only numerical.
Ronald Aylmer Fisher (1955) studied this question.