You certainly deserve my upvote. :) You set out to correct a naive statistical assumption, computed it properly, and the result was about the same (not at all

You certainly deserve my upvote. :) You set out to correct a naive statistical assumption, computed it properly, and the result was about the same (not at all common for such problems). But you posted it anyway, in the spirit of sharing useful information. As the Australians say, "Good on you, mate."