we have 2 independent groups of datas and one of them has normal distribution and the other doesn't How can I compare the means of this groups ? Paired sample T-test or wilcoxon test?
Asked
Active
Viewed 69 times
0
-
1You shouldn't base your choice on the results of normality testing of your data; see this page. See in particular this answer on the problems with using this 2-step approach of choosing the test for comparing means after you run a normality test. If group are independent, you can't do a paired t-test in any event. – EdM Dec 12 '20 at 14:28
1 Answers
0
Comment. Here are two independent samples of size $n = 200.$ The first is normal and the second is not. Both are symmetrical with the same population variance. The first has mean/median $0.6$ and the second has mean/median $0.5.$ So a two-sample Wilcoxon test appropriately detects that the two populations do not have the same center, with a very small P-value. Strictly speaking, a pooled two-sample t test would not be exact because one of the populations is non-normal.
set.seed(1212)
x = rnorm(200, .6, sqrt(1/12))
y = runif(200, 0, 1)
wilcox.test(x,y)
Wilcoxon rank sum test with continuity correction
data: x and y
W = 23737, p-value = 0.00123
alternative hypothesis: true location shift is not equal to 0
BruceET
- 56,185