Power and sample size calculations for exact conditional tests with ordered categorical data

We develop an algorithm for computing sample sizes, equal or unequal, for categorical data. We illustrate its use in the two-sample setting using the Wilcoxon rank-sum statistic, but the algorithm accommodates the entire class of linear rank statistics and can be extended to include nonlinear rank statistics as well. The sample size determinations can be based on either exact power or on a very precise Monte Carlo estimate of it. To reduce the computations further, power can be computed as a function of asymptotic critical values when the number of categories is not too small. For the Wilcoxon statistic we show that this approximation works well if there are more than five response categories.