Abstract
We propose a class of sequential nonparametric procedures for testing the hypothesis that two independent populations (treatments) have identical distributions. For this purpose, U-statistics with antisymmetric kernels are considered and their large sample approximations are derived. Based on these large sample results, two truncated sequential testing procedures allowing for random allocation of the two samples are defined. Examples of some useful antisymmetric kernels such as the sign and Gehan–Gilbert type of kernels are discussed. Using Monte Carlo simulations and a class of normal mixture distributions, the empirical Type I error, power, and average sample numbers of the test procedures proposed in this paper are compared to those of the fixed-sample t-test and O'Brien–Fleming and Pocock group sequential tests.
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