A note on sample size determination for a nonparametric test of location

Sample size determination methods are considered for hypothesis testing about location parameters of two continuous distributions using independent random samples and the Mann-Whitney-Wilcoxon (MWW) test, for a specified shift, size, and power. These methods are based on the so-called "Noether's formula," derived from a normal approximation to the power of the MWW test, and a pilot sample from each of the distributions. Compared with alternate methods, including the one using bootstrap similar to that of Hamilton and Collings (1991) the new methods are shown to be at least as good in terms of accuracy and substantially more efficient in terms of speed and variability. The simpler method, using linearly smoothed empirical cdf's of the pilot samples and requiring no bootstrapping, is recommended for practical use. Extensions and adaptations for obtaining an upper confidence bound on the sample size and to general linear rank tests are indicated. © 2006 American Statistical Association.