Parametric Test or Non-parametric Test?

#1
Let's say group A (n = 57) is independent from group B (n = 17). The distribution of group A is non-normal (Shapiro-Wilk Test p-val = 0.004) & the distribution of group B is also non-normal (Shapiro-Wilk Test p-val = 0.02). The sample size n = 57 is large enough that I can assume normality for the distribution of group A. I want to compare the distributions of group A & group B. What hypothesis test would I use? Would I use the Welch's two-sample t-test, or the Mann-Whitney U-test? Why?
 

Karabiner

TS Contributor
#2
The sample size n = 57 is large enough that I can assume normality for the distribution of group A.
The Shapiro test result told you that you should reject the Null hypothesis
that the sample B was drawn from a normally distributed population.
Your statement therefore makes no sense, I am afraid. How would a
demonstrated nonnormal distribution of a sample, or of the population
from which a sample was drawn, suddenly magically turn into a normal
distribution, just because the sample was n=57?

Since your total sample size is not small (usually n > 30 is considered
sufficient), the additional and otherwise superfluous normality assumption
for the t-test can be ignored .

I want to compare the distributions of group A & group B.
Ok, so you do not want to compare statistical parameters like means or
variances, but whether both populations are distributed similarly?

With kind regards

Karabiner