This is a very naive question: I am confused on how people test the equality of two means and two distributions.
Say that I collected the means of two populations and I wanted to test whether they were statistically different from one another.
From my perspective, testing whether two distributions are equivalent would also test whether two means are equivalent in the process.
That is, if two distributions were the same, then their means would be the same as well. Is there a difference between testing the equality of two means and testing the equality of two distributions?