Abstract #300993

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JSM 2003 Abstract #300993
Activity Number: 204
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300993
Title: Sample Size Estimation: The Bayesian, the Frequentist and the Hybrid
Author(s): Jeng Mah*+ and George G. Woodworth
Companies: Guidant/CPI and University of Iowa
Address: 3339 Owasso Heights Rd., Shore View, MN, 55126,
Keywords: Type I error ; sample size ; Bayesian ; power
Abstract:

Choice of sample size (n) is one of the major decisions that needs to be made in designing a controlled experiment. Cumulative cost and administrative difficulties prohibit excessively large experiments. One approach to sample size selection is to minimize prior expected loss. The frequentist practice of selecting a sample size to satisfy Type I and II error requirements is implied by a binary loss function. We show that the analogous Bayesian operating characteristics implied by binary loss functions are Bayesian Type I error (BTI) and Bayesian average power (BAP). Since the prior probabilities of the null and alternative hypotheses might be based on collateral information, it is not appropriate to establish default values such as .05 and .80 for BTI and BAP. We present an easily implemented Monte Carlo strategy for computing BTI and BAP and present criteria for selecting sample size based on these quantities. We show that optimal design values of BTI and BAP depend on the prior probabilities of null and alternative hypotheses and on the ratio (k) of the costs of Type I and Type II errors.

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