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In current practice, the most frequently applied approach to the handling of ties in the Mann-Whitney-Wilcoxon (MWW) test is based on the conditional distribution of the sum of mid-ranks, given the observed pattern of ties. Starting from this conditional version of the testing procedure, a sample size formula was derived and investigated by Zhao et al. (Stat Med 2008). In contrast, the approach we pursue here is a nonconditional one exploiting explicit representations for the variances of and the covariance between the two U-statistics estimators involved in the Mann-Whitney form of the test statistic. The accuracy of both ways of approximating the sample sizes required for attaining a prespecified level of power in the MWW test with arbitrarily tied data is comparatively evaluated by means of simulation. The key qualitative conclusions to be drawn from these numerical comparisons are as follows:
1. Both versions of the test maintain the level and the prespecified power with about the same degree of accuracy. 2. The sample size estimates obtained by means of the new formula are in many cases markedly lower than that calculated for the conditional test.
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