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Adjusting the -level for Sample Size

Scott M. Berry and Kert Viele

Abstract:

We review hypothesis testing results of Schervish, Seidenfeld, and Kadane (1990), Jeffreys (1961), Lindley (1972) and others that show using a constant -level across different sample sizes results in preferring an inadmissible test. We derive the rates (for testing normal means) that must decrease with to avoid preferring an inadmissible test. We show that adjusting according to these rates corresponds to performing hypothesis tests based on Bayes Factors, providing a resolution to Jeffreys's paradox.

Keywords: -level, Bayes Factor, Hypothesis Testing, Jeffreys's Paradox.