A test statistic proposal for u shaped alternatives and comparisons

One-way analysis of variance is used to compare means of two or more samples and known as ?F test?. Sometimes, the data structure is appropriate for U-Shaped Alternatives. Abebe - Singh T_r test statistic is proposed for this alternatives. In this study, a new test statistic is proposed for U-Shaped Alternatives which is based on Wilcoxon Signed Ranks Test. A numerical example is made with same data for both proposed test statistic and Abebe - Singh T_r test statistic. Afterwards these test statistics are compared according to their empirical type I error rates and power of by generating random numbers from exponential, weibull and normal distribution with different parametres.