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In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.
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