Power and Sample Size Computation with Binomial Proportions: Going Beyond Saw-Tooth Pattern

• Activity Number: 346
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Anthiyur Kannappan*+ and Cyrus Mehta and Pralay Senchaudhuri
• Companies: Cytel Inc. and Cytel Inc. and Cytel Inc.
• Keywords: power ; sample ; size ; saw-tooth ; binomial ; proportion

Abstract

It is well known that in the case of power & sample size computations with binomial proportions, there exists a phenomena of saw-tooth pattern in the power vs sample size curve. What this pattern indicates is that there is an 'anomalous' situation where the power of an experiment may decrease with an increased sample size. The reason for this seemingly anomalous situation is also known, that the discreteness of binomial distribution precludes computation of sample size to the exact value of alpha specified. Nevertheless, the overwhelming perception among statisticians is that saw-tooth pattern is an inherent anomaly present in power computation with binomial proportions. One way to counteract this perception is to present the computation of power not as a function of a single variable (viz.) sample size but as a function of two variables - sample size and 'attainable' alpha. This leads to a three dimensional graphical representation involving sample size, 'attainable' alpha, and power, where it can be easily visualized and understood that there is no anomalous situation present in power computations with binomial proportions. This paper presents several illustrative examples.