> I think what I implied (and others are trying to communicate across) is how do we know the galaxies are independent variables as you claim? Simple. I never

> I think what I implied (and others are trying to communicate across) is how do we know the galaxies are independent variables as you claim? Simple. I never claimed that the random variables were independent. Instead I just observed that if one made an ASSUMPTION of independence (and the rest of i.i.d.) then could use the theorem the law of large numbers and get a result without being concerned with what fraction the sample size was of the whole population. I didn't even try to argue that there was independence or even approximate independence. The independence assumption is really common in applications of probability and statistics. Maybe then people comfort themselves by believing that independence holds approximately and close enough. As I recall, there has been at least one attempt to investigate approximate independence, but that work is likely not well known. Questioning independence in this discussion of cosmology is appropriate. Again, in practice, an independence assumption is common, and with all of "i.i.d." could apply the strong law of large numbers and get results about a large population from a comparably small sample thus responding to the stated concern I was responding to: > ... a frighteningly small sample to draw conclusions from?