# How combine two statistics from different tests?

I have a case in which I have two sets of ranks. To compare these two ranks, I use once wilcox test and once ks test. The reason why I am using both returns to the special cases of shapes of data which cannot be detected by using only one of these tests. At the moment, I am getting the minimum p-value from these two tests and it works okay. However, I know that this is not correct way. Also, since the p-values come from dependent and different tests p-value combination methods also wont work here.In the results I see two reported statistics as well. Should I use those? how can I get single value (statistic and p-value) from these two tests? Any suggestion would be appreciated.

• How you should combine them* depends on what you want to detect, precisely, which should be given by a single, clear alternative hypothesis. $\quad$ * .. where combine two very different statistics makes sense at all; it's not at all clear that it does in this instance. Mar 2 at 5:28
• @Glen_b You can have a look into link. I need to detect both differences in my data meaning both are equally important. So I am using two tests at the same time.
– Nmgh
Mar 2 at 5:45

The simplest approach, but also most conservative, is to use a Bonferroni correction. In your case, this would be simply using $$2 \times \text{min}(p_1, p_2)$$, where $$p_1$$ and $$p_2$$ are the p-values from each test.