## Adjusting the alpha-level for Sample Size

September, 1995

Tech Report

### Author(s)

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 $$\alpha$$-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.