On Tue, 01 Oct 2002 12:49:51 +0100, Thom Baguley <[EMAIL PROTECTED]> wrote:
> Donald Burrill wrote: > > And, to address your last question, a Mann-Whitney test (aka a Wilcoxon > > rank-sum test) is exactly equivalent to a t-test on the mean ranks; so > > yes, you can, but use alpha/2 for your tabled significance level. > > Pedantry alert! Is it _exactly_ equivalent - don't the results > differ very slightly (though not to a degree that would make a > difference in practice)? I think I remember the details from what DB cites - Conover, W.J. & Iman, R.L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics. _The American Statistician, 35,_ 124-129. When there are no ties, the t-test computed on ranks gives exactly the same *ordering of outcomes* as you would tabulate by hand. So you can *compute* the t-test. If you look up the tabled value for t (so-many d.f.), you get a good approximation to the p-value. If you compute a t-value for all the permutations of the samples, and assign the p-value according to the extreme, then you get the same p-value, exactly. The large-sample tests on ranks often use normal-approximation instead of t-test approximation, since "the variances are known." However, variance estimates are not precise if there are ties. So the alternate tests are no longer precise or exact. Simple t-tests or F-tests on the ranked data gave answers that were generally as accurate, and their errors tended to be on the conservative side (not-significant)(which is good). -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
