  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.
