Some tests for detecting trends based on the modified Baumgartner–Weiß–Schindler statistics

We propose a modified nonparametric Baumgartner–Weiß–Schindler test and investigate its use in testing for trends among K binomial populations. Exact conditional and unconditional approaches to p-value calculation are explored in conjunction with the statistic in addition to a similar test statistic proposed by Neuhäuser (2006), the unconditional approaches considered including the maximization approach (Basu, 1977), the confidence interval approach (Berger and Boos, 1994), and the E+M approach (Lloyd, 2008). The procedures are compared with regard to actual Type I error and power and examples are provided. The conditional approach and the E+M approach performed well, with the E+M approach having an actual level much closer to the nominal level. The E+M approach and the conditional approach are generally more powerful than the other p-value calculation approaches in the scenarios considered. The power difference between the conditional approach and the E+M approach is often small in the balance case. However, in the unbalanced case, the power comparison between those two approaches based on our proposed test statistic show that the E+M approach has higher power than the conditional approach.