# Go with t-test or Mann-Whitney U test?

I'm measuring performance of 2 methods (method_A and method_B) that try to satisfy customers demands. Both methods produce results between 0 (none of the demands were satisfied) and 1 (all demands were satisfied). Also, both methods run for a certain amount of Time and, after that, they return best possible solution.

I've generated 30 datasets and solved each one with method_A and method_B with different Time limits. The results are summarized below:

My goal is to do some hypothesis testing with the results. I've considered to do a t-test but before that I've decided to do some normality tests. Results below:

Histogram of method_A and method_B

Q-Q Plot and Shapiro–Wilk test for method_A

Q-Q Plot and Shapiro–Wilk test for method_B

For small Time values data seem to follow normal distribution so I think that t-test can be done. Am I right? However, when Time values are large the distribution seem to become non normal. This is especially visible when average results of both methods are close to 1:

• Time equal to 80 and 90 for method_A
• Time equal to 140 and 150 for method_B

So the question is: For these scenarios should I do Mann-Whitney U Test? For some reason, doing 2 different tests (t-test and Mann-Whitney U Test) for same data doesn't seem right...

Overall, what is the best way to do hypothesis testing with this kind of data?

• Yeah, I'm also inclined to follow the "safety first" principle and just use Mann-Whitney test and be done with. Thanks – user3541395 May 17 '19 at 10:12