Abstract:
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Standard procedures for testing equality between two population proportions can be easily found in most introductory statistics textbooks. Keith and Fligner (1977) discuss the asymptotoic efficiency of two procedures by use of pooled and nonpooled sample variances for testing equality of two proportions for two-sided test. However, the discussion for one-sided test ($H_0: P_1 \ge P_2$ VS $H_1: P_1 < P_2$) is limited. In this paper, we discuss the performance of the pooled and nonpooled sample procedures for a specified nominal level. A general guideline is that when the sample sizes are approximately equal, the estimated type I error, using pooled sample variance, will be closer to the nominal $\alpha$ level than using the nonpooled sample variance.
On the other hand, when $n_1$ is much larger than $n_2$, and both $P_1$ and $P_2$ are small, or $n_1$ is much smaller than $n_2$ and both $P_1$ and $P_2$ are large, then the estimated type I error using the nonpooled sample variance is closer to the nominal $\alpha$ level. Simulation studies are presented to demonstrate the findings. The power under both procedures is discussed.
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