Scheffe's more powerful F-protected post hoc procedure

In 1970 Henry Scheffe proposed a more powerful version of his well known post hoc multiple comparison procedure, only to fail to recommend it by the paper's end. The point of the current paper is to bring this simple modification to a wider audience, complete with an original derivation, in hopes that the method will be embraced by researchers despite its creator's hesitations. Specifically, whereas Scheffe's original (1953) procedure advocates testing any exploratory post hoc contrast or comparison using a critical value assuming k - 1 between-group degrees of freedom, Scheffe's later modification (1970) will be demonstrated here showing that a more liberal critical value assuming k - 2 between-group degrees of freedom may be used if an omnibus null hypothesis across all means has been rejected.