Robustness and efficiency of some tests for ordered alternatives in the C-Sample location problem

For the c-sample location problem with ordered alternatives we compare a test proposed by Barlow et al. (1972) and its Welch modification for the case of unequal variances with some nonparametric counterparts, the Jonckheere test and modifications of the Jonckheere test. In these modifications the Mann-Whitney statistic is replaced by other two-sample linear rank statistics. The comparison is referred to the actual level and the power of the tests and it is carried out via Monte Carlo simulation assuming short-, medium- and long-tailed as well as asymmetric distributions. It turns out that in the case of unequal variances and symmetric distributions the Welch modification of the test of Barlow et al is the most α-robust test among the tests considered, but for equal variances special Jonckheere-type tests are to be preferred.