Tests of Significance Violate the Rule of Implication

Abstract
The rule of implication, (+) If hypothesis H implies hypothesis I, then evidence sufficient to warrant the rejection of I, in turn warrants the rejection of H, is a very plausible principle of inductive inference. It is shown that significance tests violate this principle. Two ways to account for this violation are considered; neither account is fully satisfactory. First, a distinction might be made between the absolute degree of confirmation and the change in the degree of confirmation due to a specific result. Measures of the change in the degree of confirmation need not obey the rule of implication. Unfortunately, it is difficult to interpret significance tests as a measure of the change in degree of confirmation of an hypothesis. Second, it might be observed that hypotheses are sought that are informative as well as faithful to observations. Amalgamating a measure of informativeness with a measure of faithfulness can result in violations of the rule of implication. Unfortunately, it is unclear why significance tests amalgamating measures of informativeness and faithfulness are desirable.
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