On the use of Spearman's correlation coefficient for testing ordered alternatives

This paper proposes a nonparametric test for detecting ordered alternatives in a completely randomized design. In short, the test statistic is the sum of all possible Spearman correlation coefficients calculated across all samples simultaneously. The exact mean and variance of the null distribution are derived and it is shown that this distribution is asymptotically normal. Furthermore, a small sample simulation study which compares the proposed test to some existing tests is presented. The results of the study indicate that the proposed test is more powerful for certain combinations of sample sizes, location configurations, and population distributions. In addition, an actual data set is analysed.