Simple, Powerful Statistics: An Instantiation of a Better ‘Mousetrap’
R.S. Rodger fully developed, more than three decades ago, probably the most powerful methodology which exists for detecting real differences among population means (μ’s) following an analysis of variance. Since it is a post hoc method, a theoretically infinite number of potential statistical decisions may be considered, but Rodger’s method limits the final number of decisions to a single set which contains exactly J-1 (i.e., v1, the number of means in a study minus one) of them. It also constrains the number of these J-1 decisions that may be declared statistically “significant.” Rodger’s method utilizes a decision-based error rate, and ensures that the expected rate of rejecting null contrasts that should not have been rejected (i.e., the type 1 error rate) will be less than or equal to either five or one percent, regardless of the number of contrasts examined by a researcher prior to finally deciding upon the scientifically optimal set of decisions.
The greatest virtue of Rodger's method, though, is not its considerable power, but its explicit specification of the magnitude of the differences that the researcher will claim to exist among the population parameters. The implied true means that this method calculates are the theoretical population μ’s that are logically implied, and mathematically entailed, by the J-1 statistical decisions that the researcher has made. These implied true means can assist other researchers in confirming or disconfirming population parameter claims made by those who use Rodger’s method. A free computer program (SPS) that instantiates Rodger’s method, and thereby makes its use accessible to every researcher who has access to a Windows-based computer, is available from the author.
Keywords: Rodger’s post hoc analysis method, decision-based error rate expectation Eα, non-traditional test criterion F[Eα], implied true μ’s, SPS computer program