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Abstract:
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A variation on partition testing is proposed as a new paradigm for testing. As is well known (cf. Lehmann, 1959), a confidence set is equivalent to a family of hypothesis tests. Correspondingly, a standard approach for constructing confidence sets is to test each point in the parameter space. Under the proposed testing paradigm, a single test likewise involves testing each point in the parameter space--not just those corresponding to a null hypothesis. Consequently, the conclusion of such a test is a confidence set--a more informative inference than rejecting or failing to reject a null hypothesis. Furthermore, the proposed testing paradigm controls not only the probability of making a Type I error, but more generally the probability of making any false assertions, with no loss of power relative to traditional hypothesis testing. Examples are provided.
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