An Order Statistic for Coarse Measurement Scales: Ce Derived from U

The present study was concerned with the behavior of the Mann-Whitney U test with coarse measurement scales, which are scales having relatively few values. The Monte Carlo method with at least 8000 replications was used. The scales examined ranged from a scale with two values to a scale with 2048 values. Because of the high probability of ties, serious disturbances in the U were obtained for scales having 16 values or less. If the procedures and tables outlined in standard texts were used to analyze experimental results, the outcomes would be in error. The Type I error would be overstated, and the Type II error would be understated. Ce, an empirically derived statistic analogous to U but incorporating the scale grain as a parameter, is described. Typical tables of critical values are presented. Extended tables of critical values and the cumulative distribution functions for Ce are available.