What to do when comparing mean of two populations and one is not normal? I have a dataset with two populations (unpaired). First one with 36 observations, second one 74.
The first passes the Shapiro normality test with p-value = 0.1521, the second fails it with p-value = 0.01551.
I would like to perform a test t.test(first, second), how can I do? If I transform with a BoxCox the second population it doesn't make any more sense to compare it with the first population.
Edit:
Here is the data asked by @BruceET
> lapply(g, function(x) c(mean=mean(x), var=var(x), sd=sd(x)))
$mark
     mean       var        sd 
21.986111  6.364087  2.522714 

> lapply(p, function(x) c(mean=mean(x), var=var(x), sd=sd(x)))
$mark
     mean       var        sd 
25.378378  7.608293  2.758313 




If normality is heavily violated, you can consider non-parametric methods that do not make assumptions about population distributions. Usually, there is a non-parametric equivalent to common problems like the two-sample t-test where the two samples are independent. In this case, you can use a very general Mann-Whitney test.
