Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Adjusting the alpha-level for Sample Size

Publication Date

September, 1995

Publication Type

Tech Report


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 \(\alpha\)-level across different sample sizes results in preferring an inadmissible test. We derive the rates (for testing normal means) that \(\alpha\) must decrease with n to avoid preferring an inadmissible test. We show that adjusting \(\alpha\) according to these rates corresponds to performing hypothesis tests based on Bayes Factors, providing a resolution to Jeffreys's paradox.