Fool’s Type IIa Error Revisited
AbstractIn carefully examining the thesis of a paper by Anderson, Nelson, and Edgington (1984) concerning the socalled Fool’s Type IIa error, one realizes that certain fundamental statistical tenets have been overlooked or ignored. The purpose of the present paper is to discount the notion of a Fool’s Type IIa error under the Neyman-Pearson philosophy of testing statistical hypotheses and to highlight the need for improved statistical education related to hypothesis testing. If the importance of Type I and Type II errors cannot be quantified, then the Neyman-Pearson approach to hypothesis testing is of no value, and hence a Fool’s Type IIa error is irrelevant. If statistical testing errors are important and can be quantified, then adjustment for the Fool’s Type IIa error region is equivalent to increasing the probability of making a Type I error.