A modified Wilcoxon test for non-negative distributions with a clump of zeros

Comparing two samples with a continuous non-negative score, e.g. a utility score over [0, 1], with a substantial proportion, say 50 per cent, scoring 0 presents distributional problems for most standard tests. A Wilcoxon rank test can be used, but the large number of ties reduces power. I propose a new test, the Wilcoxon rank-sum test performed after removing an equal (and maximal) number of 0's from each sample. This test recovers much of the power. Compared with a (directional) modification of a two-part test proposed by Lachenbruch, the truncated Wilcoxon has similar power when the non-zero scores are independent of the proportion of zeros, but, unlike the two-part test, the truncated Wilcoxon is relatively unaffected when these processes are dependent.