# Test which test to use: (Student-) T-test or (Mann-whitney) U-test

I've seen a couple of questions here around this alternative, but a -very basic- specific question I cannot answer from the top of my mind.

Having a metric measure $$M$$ taken before treatize and after treatize, I want to test the difference as the therapeutic effect in two groups, say material of therapeutic instrument is (k)eramic or (p)lastic.

The design is thought as first computing the difference $$M_d=M_{after}-M_{before}$$ and consider T-testing of $$M_d$$ over the two independent groups, call them $$K$$ and $$P$$.

But T-testing assumes normal distribution in the data, which might be violated or un-guaranteed when

• a) $$M_d$$ is not normal,
• b) $$M_d$$ in either group is not normal,
• c) $$N$$ (or only $$N_1$$ or $$N_2$$) is too small to confirm normality.

But do I have to test before normality of $$M_d$$ the same test on the $$M_{after}$$ and $$M_{before}$$ in their subgroups?

The problem is on a couple of similar items and subgroups, and the subgroups have $$N$$ between, say 30 and 70.

I assume, that after only one of the conditions in a)...c) are not met, I have to use the Mann-Whitney-U-test on $$M_d$$.

Is this correct or is this overkill in testing at all? (I'm tempted to simply use U-test, because the $$N$$ are somehow in the near of the lower limit of size of subgroups.)

• Christian - thanks for your link to your other answer, it is a good consideration. However I don't know how to use it in answering the sub-question whether it sufficies to test the normality of $M_d$ in the whole group or in the two subgroups separately, and as well with $M_{after}$ and $M_{before}$. In this hindsight it's also a technical question... Nov 22 '21 at 20:44