Two Sample Order Free Trend Inference with an Application in Plant   Physiology
  This work is motivated by a biological experiment with a split-plot design, for the purpose of comparison of the changing patterns in seed weight from two treatment groups as subgroups in each of the two groups subject to increasing levels of stress. We formalize the question into a nonparametric two sample comparison problem for changes among the sub samples, which was analyzed using U-statistics. Zero inflated value were also considered in the construction of the U-statistics. The U-statistics were then used in a Chi-square type test statistics framework for hypothesis testing. Bootstrapped p-values were obtained through simulated samples. It was proven that the distribution of the simulated sample can be independent provided the observed samples have certain summary statistics. Simulation results suggest that the test is consistent. 
Yishi Wang, Ann E. Stapleton, Cuixian Chen
stat.ME