> This has nothing to do really with the question that Troels asked, > but the exposition quoted from the AA paper is unnecessarily > confusing. > The phrase ``Because X0 and X1 have identical marginal > distributions ...'' > throws the reader off the track. The identical marginal distributions > are irrelevant. All one needs is that the ***means*** of X0 and X1 > be the same, and then the null hypothesis tested by a paired t-test > is true and so the p-values are (asymptotically) Uniform[0,1]. With > a sample size of 100, the ``asymptotically'' bit can be safely ignored > for any ``decent'' joint distribution of X0 and X1. If one further > assumes that X0 - X1 is Gaussian (which has nothing to do with X0 and > X1 having identical marginal distributions) then ``asymptotically'' > turns into ``exactly''.
Another related issue is that uniform distributions don't look very uniform: hist(runif(100)) hist(runif(1000)) hist(runif(10000)) Be sure to calibrate your eyes (and your bin width) before rejecting the hypothesis that the distribution is uniform. Hadley -- http://had.co.nz/ ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
