if we compare two stocks, which should be used, difference between means or mean of difference? It is said that the system risk of stocks assumed to be the same, so they can not be indepent, if so, whether we should use “the mean of difference”? Appreciate very much foryour time!

mean of difference would be a completely new probability distribution wouldn’t it? I think difference of means, and significance of that is what is to be used. But I could be wrong.

i say difference btw means… which is basically stating what is the diff. btw the average return on the 2 stocks

I am not sure about your question, but the basic distinction between difference of means or mean of differences is whether there is an explicit pairing of the observations. If observation #1 in, say, the control group goes with observation #1 in the experimental group it’s mean of differences. If each group is just a pile of observations, then it is difference of means.