Two Stage Approach Based on Welch Statistic for Multiple Comparisons of k Binomial Proportions for Small Sample

Abstract

Multiple comparisons of k independent binomial proportions ( k > 2 ) are studied when the proportions p_i , i =1,2,3,...,k are close to zero. Several tests perform poorly in terms of the pairwise error rate (PWER) and the familywise error rate (FWER) when the proportions p_i , i =1,2,3,...,k are close to zero. This problem is an issue that seems to have been overlooked. Even though several tests have been proposed, they cannot perform well in terms of PWER and FWER. From the above problems, we proposed a procedure of multiple comparisons for examining the difference between k independent binomial proportions which is the proposed two-stage approach based on Welch statistic. For comparing the performance of test statistics for multiple comparisons, the proposed two stage approach is compared with the two-stage approach under PWER, FWER and the estimated pairwise powers. Our results were evaluated by using Monte Carlo simulation. The results indicated that the performance of the proposed two stage approach can protect PWER and FWER better than the two-stage approach. In cases of the estimated pairwise power, the proposed two stage approach and the two-stage approach have similar estimated pairwise power. Our study suggests the proposed approach for multiple comparisons because the proposed two-stage approach can protect PWER and FWER, and the estimated pairwise power is quite well.