Dr Campbell and colleagues outline some ways of calculating sample sizes in two group comparisons for binary, ordinal, and continuous outcomes [1]. While the presented formulas for binary and continuous data are well-known and have been repeatedly reviewed in the statistical [2,3] as well as in the medical literature, [4,5] the proposed proceeding to estimate sample sizes for the Wilcoxon-Mann-Whitney U test for ordinal response seems to be the only new issue of the paper. However, the proposed formula, which uses an odds ratio as effect size, is quite complicated. For application a number of steps are required, which are circumstantial and troublesome in practice. In this note I want to point out that the estimation of sample sizes for ordinal data can be much easier.
Let X and Y be the ordinal outcomes in the two groups, then the probability p=P(X<Y) that the response in
one group is smaller than in the other contains similar information as the standardised difference of
means for continuous data [6]. Hence, it is obvious to use p as effect size. A corresponding
formula is given by Noether [7]. The probability p can either be chosen arbitrarily similar to
the clinically relevant difference in the continuous case or can be estimated from a pilot sample by
means of the Mann-Whitney statistic U [6]. For the data shown in table V one can calculate U=317
and p=317/(21×22)=0.686. Using Noether's formula [2,7] the sample size is m=38 patients per
group. The use of an odds ratio as effect size is possible due to the simple relation