Power estimation for testing normal means

Abstract

We examine the validity of the observed power using the estimation approach. Under a robust Bayesian framework, we show that the observed power for testing normal means overestimates the power for significant data yet underestimates the power for insignificant data. This phenomenon persists for one-sided and two-sided problems. Some misinterpretations of the observed power are discussed.

Keywords:

• observed power
• p-value
• power
• robust Bayesian analysis
• sample size calculations

MSC 2000 :

• Primary: 62F03
• 62F35
• Secondary: 62F15
• 62C10

Acknowledgements

The authors would like to thank Prof. H. Wang and Prof. J.-S. Wu for their helpful comments and suggestions that inspired this study. Thanks also to the anonymous referee for the helpful review that improved the presentation of this paper. The research is supported by Taiwan NSC 91-2118-M-259-003 and NSC 91-2118-M-259-002