On Power Approximations and Comparison of Several Asymptotic Tests to Detect a Specified Difference between Two Proportions

Abstract

A large sample test is proposed for a problem of testing for a specified difference between two binomial proportions. The test is compared to the tests by Falk and Koch (1998), and Parmet and Schechtman (2007), and is shown to dominate in terms of the Type I error rate control. Asymptotic power is derived for each test and is shown to result in values quite proximate to the simulated power values. In addition, formulas to perform sample size estimation are provided. These methods are expected to be especially valuable in the design stage when obtaining the correct power/sample size estimation is essential.

Keywords:

• Binomial tests
• Large-sample test
• Non-inferiority problem
• Normal approximation

Mathematics Subject Classification:

• Primary 62E20, 62F03, 62F05, 62P10
• Secondary 62Pxx