Concept Clarification: Wilcoxon rank test vs two-samples T-test (UPDATE) I am currently deciding whether to use the Wilcoxon rank test vs two-samples T-test to assess BMI between two unrelated groups. Using the following code to assess normality with(group1, shapiro.test(BMI)), I got p > 0.05 for group 1 (n = 10) but p < 0.05 for group 2 (n = 50).
I want to know whether this means I should use a non-parametric test for my analysis? I know if both are p < 0.05, then I should definitely use the Wilcoxon rank test BUT I have no clue what to do when only one group is non-normally distributed.
UPDATE: QQ-PLOT FOR GROUP 2


Following standard logic, the t-test assumes normality in both groups, so if you reject it in one, that should be reason enough to think that there's something wrong with the normality assumption.
Unfortunately, though, it is not quite as simple as that, and "standard logic" is somewhat flawed. In fact, even for certain non-normal distributions, the t-test is better than the Wilcoxon test. Testing whether the data are normal or not solves the wrong problem. Model assumptions are never fulfilled anyway (this holds as well for Wilcoxon, still which assumes i.i.d. at least), and the really relevant issue is whether there is something in the data that may mislead the t-test, such as gross outliers or strong skewness. This can only be diagnosed from looking at the data, a Shapiro-Wilk test won't tell you this.
