BEHAVIOR OF THE ASYMPTOTIC POOLED Z-STATISTIC

Félix Almendra-Arao (Mexico)

Received August 5, 2009

Abstract

In the literature, there are many references to the asymptotic non-inferiority test that uses Z-statistic with pooled variance, but in none of these papers are the test sizes computed. However, it is important for asymptotic tests to determine behavior of test sizes, especially to determine whether the test is liberal or conservative, and if the test is conservative, to measure how conservative it is. In this study, non-inferiority test sizes are calculated for the difference between two independent proportions based on Z-statistic with pooled variance, for several continuity corrections, and the behavior of these test sizes is analyzed. Sample sizes  are examined with nominal significance levels  and non-inferiority margins .1, .15 for the test without continuity correction as well as that with five continuity corrections. For sample size configurations, nominal significance levels and non-inferiority margins, the test sizes of the asymptotic pooled Z-statistic with the continuity corrections considered are erratic.

Keywords and phrases: non-inferiority test, binomial proportion, test size, asymptotic test.