Type I Errors and Their Decision Basis

It is proposed that an error‐rate 1 should be set for each statistical decision to be made. Methods for testing statistical hypotheses in the context of analysis of variance are reviewed and evaluated from the decision‐based error‐rate viewpoint. If decisions are the proper bases for the choice of an error‐rate, the available methods for testing any or all linear contrasts or linear functions of the means are unacceptable. Two new methods (R and D) are proposed for testing all contrasts or linear functions. One implication of the arguments given here is that, for most purposes, research workers have been using the wrong tables of F to test their statistical hypotheses.