Adjusting the -level for Sample Size
Scott M. Berry and Kert Viele
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.
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