I am comparing the size distribution of trees in six pairs of plots where one plot received a treatment and the other a control. Using a Kolmogorov-Smirnov test on each pair of plots I find that $p$ ranges from $0.0003707$ to $0.75$. Are there any appropriate methods for dealing with all of the replicates together, such as a multi-sample extension of the KS test, or is there an appropriate follow up test? Or should I just conclude something like “The size distribution differ significantly $(p < 0.05$) in 2 pairs of plots and marginally ($p = 0.59$) in one pair of plots.”

**Answer**

There actually are some multiple sample KS Tests. E.g., an r-sample Kolmogorov-Smirnov-Test with $r\geq 2$ which, I believe, has good power. A preprint of that beautiful paper is available here. I also know of K-Sample Analogues of the Kolmogorov-Smirnov and Cramer-V. Mises Tests (but they have less power as far as I know).

**Attribution***Source : Link , Question Author : N Brouwer , Answer Author : Momo*