On Tue, 1 Oct 2002, Thom Baguley 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)?
Pedantic reply: My proximate source is quoted below. If you want more details, consult Donald Zimmerman or Bruno Zumbo. (Bruno, I believe, used to subscribe to this edstat list; I don't know if he still does.) As I read their prose, the equivalence is exact for the large-sample normal approximation. If the "differ very slightly" Thom has in mind reflects whatever difference there is between the true distribution and the normal approximation thereto, he's probably right; and he's certainly right, I think, that it would not affect practice. -- DFB. >From Donald W. Zimmerman & Bruno D. Zumbo, "The relative power of parametric and nonparametric statistical methods", Chapter 19 in _A Handbook for Data Analysis in the Behavioral Sciences_, edited by Gideon Keren and Charles Lewis (Erlbaum, 1993), pages 487-488: "It has been known in mathematical statistics and recently emphasized by Conover (1980), Conover and Iman (1981), and others, that the Wilcoxon-Mann-Whitney test in standard form, that is the large sample normal approximation, is equivalent to an ordinary Student _t_ test performed on the ranks of measures instead of the measures themselves. [They then give an equation expressing _t_ in terms of _W_ and _N_.] ... "This means that, apart from details of computation, it makes no difference whether a researcher performs a Wilcoxon test based on rank sums, or alternatively, pays no attention to _W_ and simply performs the usual Student _t_ test on the ranks ... "[Similarly], the Wilcoxon matched-pairs signed-ranks test is equivalent to a paired-samples Student _t_ test on signed ranks instead of original signed differences. The Kruskal-Wallis test is equivalent to an ordinary _F_ test performed on the ranks of the measures in an ANOVA design instead of the measures themselves, and so on. These findings have not received a great deal of attention in introductory statistics textbooks and are not widely known among researchers in psychology." The references are Conover, W.J. (1980). _Practical nonparametric statistics_ (2nd ed.). New York: Wiley. Conover, W.J. & Iman, R.L. (1981). Rank transformations as a bridge between parametric and nonparametric statistics. _The American Statistician, 35,_ 124-129. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 [Old address: 184 Nashua Road, Bedford, NH 03110 (603) 471-7128] . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
