hypotheses suggested by the data, if tested using the data set that suggested them, are likely to be accepted even when they are not true. This is because circular reasoning would be involved: something seems true in the limited data set, therefore we hypothesize that it is true in general, therefore we (wrongly) test it on the same limited data set, which seems to confirm that it is true. Generating hypotheses based on data already observed, in the absence of testing them on new data, is referred to as post hoc theorizing.
The correct procedure is to test any hypothesis on a data set that was not used to generate the hypothesis.
For Post Hoc analysis of ANOVA,
Henry Scheffé's simultaneous test of all contrasts in multiple comparison problems is the most well-known remedy in the case of analysis of variance.1 It is a method designed for testing hypotheses suggested by the data while avoiding the fallacy described above.
So I was wondering how Scheffé's test avoids the fallacy of data snooping?