The various components of this methodology were fully worked out by R. S. Rodger in the 1960s and 70s, and seven of his articles about it were published in the British Journal of Mathematical and Statistical Psychology between 1967 and 1978.
[1][2][3][4][5][6][7] Statistical procedures for finding differences between groups, along with interactions between the groups that were included in an experiment or study, can be classified along two dimensions: 1) were the statistical contrasts that will be evaluated decided upon prior to collecting the data (planned) or while trying to figure out what those data are trying to reveal (post hoc), and 2) does the procedure use a decision-based (i.e., per contrast) error rate or does it instead use an experiment-wise error rate.
This was an especially important consideration in the present experiments in which interesting conclusions could rest on null results" (Williams, Frame, & LoLordo, 1992, p.
Rodger's method permits an absolutely unlimited amount of post hoc data snooping and this is accompanied by a guarantee that the long run expectation of type 1 errors will never exceed the commonly used rates of either 5 or 1 percent.
Whenever a researcher falsely rejects a true null contrast (whether it is a planned or post hoc one) the probability of that being a type 1 error is 100%.
"An error occurs, in the statistical context, if and only if a decision is made that a specified relationship among population parameters either is, or is not, equal to some number (usually, zero), and the opposite is true.
As Bird stated: "Rodger (1965, 1967a, 1967b, 1974) explored the possibility of examining the logical implications of statistical inferences on a set of J − 1 linearly independent contrasts.