Application of Anbar's Approach to Hypothesis Testing to Detect the Difference Between Two Proportions

• Activity Number: 71
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Ananya Roy*+ and Julia Soulakova
• Companies: University of Nebraska-Lincoln and University of Nebraska-Lincoln

Abstract

We discuss Anbar's(1983) approach for estimating a difference between two binomial proportions with respect to a hypothesis testing problem. Such an approach results in two possible testing strategies. While the results of the tests are expected to agree for a large sample size when two proportions are equal, the tests are shown to perform quite differently in terms of their probabilities of a type I error for selected sample sizes. Moreover, the tests can lead to different conclusions, which are illustrated via a simple example; and the probability of such cases can be relatively large. We propose a modified test and assess the performance of this test compared to the conventional test based on normal approximation. The modified Anbar's test is shown to control the probability of a type I error better for moderate sample sizes.