I have a set of medical data which contains two samples taken in different time periods. Although the samples do not strictly contain the same people in each group, a large proportion in each group are the same.
My question, is that I have thus far computed a
ks.test in R to compare the distributions of the two groups to determine if they're significantly different. This test was used since the data are not normally distributed and I wanted to check for more than just mean differences, but also look at the variance and shape of the distribution which is a result of the Kolmogorov Smirnoff test (as opposed to the t test).
The result from this test was that the distributions are significantly different. Therefore, my question is, if I were to then filter for all of the people who appear in both groups and conduct a paired t test on the differences (which are normally distributed), would it automatically follow that the difference is significantly different to zero? In other words, is there a rule which says that if the distributions of the two groups are significantly different (using the sample of people who appear in both groups), then this must mean that the per person differences are significantly different to 0?
I understand that this wouldn't work the other way, i.e. if the paired t test was significant, then this wouldn't necessarily mean that the KS test would be significant.
Is that correct?