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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?

m gh
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    You shouldn't base your choice on the results of normality testing of your data; see [this page](https://stats.stackexchange.com/q/2492/28500). See in particular [this answer](https://stats.stackexchange.com/a/30053/28500) 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

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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
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