I have two groups: A and B. Based on QQ plot and Shapiro-Wilks test, both A and B are not normally distributed. I have included the histogram images below for further context.
A has a sample size of 3068, and B has a sample size of 1981.
The variance for A is 278.3801 while B's is 281.8245.
The variables being compared are independent.
I am conflicted whether or not to use t independent test or Wilcoxson's Rank Sum test. The argument for using the t independent test is because the sample size is large enough to apply the Central Limit Theorem.
On the other hand, I am leaning towards Wilcoxson's Rank Sum test because the sample size of the two groups are drastically different (3068 vs 1981), and the distribution for both groups are non-normal.
Which test do you think you would use? It would also be great to give your explanation as to why you choose the test. Thank you.
Additional context:
Shapiro-Wilk normality test
For A: W = 0.97652, p-value < 2.2e-16
For B: W = 0.97989, p-value = 4.384e-16
Histogram
EDIT
Ho: There is no difference in between A and B.
Ha: There is a difference between A and B.
summary(A)
Min. 1st Qu. Median Mean 3rd Qu. Max.
17.00 35.00 50.00 48.84 62.00 90.00
summary(B)
Min. 1st Qu. Median Mean 3rd Qu. Max.
18.00 38.00 53.00 51.33 64.00 90.00
Levene's Test
group coerced to factor.Levene's Test for Homogeneity of Variance (center = median)
Df F value Pr(>F)
group 1 0.2123 0.645 5047