For example,
\begin{array} {|r|r|}\hline & \text{Sample}\enspace X & \text{Sample}\enspace Y \\ \hline mean & 14 & 20 \\ \hline median & 5 & 5 \\ \hline \end{array}
How should we approach in order to test if $mean_Y > mean_X$ is statistical significant?
My thought is: It seems that the variables in the 2 groups don't follow a normal distribution (mean != median). But if the sample size is large enough, we can use the two-sample t-test (parametric). However, if our sample size is too small, we should use Wilcoxon-Mann-Whitney (or rank sum) test (non-parametric).
Is that a good approach? Not sure if I'm missing anything here.
Thank you!