Thanks Peter, You are correct! After I sent the previous message, I realized that I was comparing the sign test against the Wilcoxon test. I would have replied sooner, but I realized that while I was out walking my dogs. CHV   Charles H Van deZande -------Original Message------- From: Peter Dalgaard Date: 05/19/09 10:32:30 To: Charles Van deZande Cc: r-help@r-project.org Subject: Re: [R] Wilcoxon nonparametric p-values Charles Van deZande wrote: > Thanks Peter, > There are 8 measurements less than 8.5, so calculating the probability > (binomial) of 8, or fewer, happening by chance with n = 20 and p = 0.50 > gives P = 0.25-- the book answer. I've tried several problems in other > textbooks and in each case I get vastly different P-values than I get > with wilcox.test or wilcox.exact. Ah, but that is NOT a signed-rank test, just a sign test. (Using the former as a test of the median is BTW not really a good idea unless you assume symmetry of the distribution.) It is also still a one-sided test, with two tails you get > binom.test(8,20) Exact binomial test data: 8 and 20 number of successes = 8, number of trials = 20, p-value = 0.5034 alternative hypothesis: true probability of success is not equal to 0.5 95 percent confidence interval: 0.1911901 0.6394574 sample estimates: probability of success 0.4 (and that is disregarding that one observation is exactly 8.5, so you should really look at 7 in 19 rather than 8 in 20.) > However, upon further testing, I've found good agreement when the > calculated P-values are small, but disagreement when P-values are > large. This might mean a problem with wilcox.test and wilcox.exact when > P-values are large or I might be misinterpreting something. You need to read some more theory. The extreme cases (all signs equal) are equally unlikely for the sign test and the signed-rank test. > CHV >   > Charles H Van deZande > /-------Original Message-------/ > > /*From:*/ Peter Dalgaard <mailto:p.dalga...@biostat.ku.dk> > /*Date:*/ 5/19/2009 5:35:07 AM > /*To:*/ cvandy <mailto:cvand...@gmail.com> > /*Cc:*/ r-help@r-project.org <mailto:r-help@r-project.org> > /*Subject:*/ Re: [R] Wilcoxon nonparametric p-values > > cvandy wrote: > > When I use wilcox.test, I get vastly different p-values than the problems > > from Statistics textbooks. > > For example: > > The following problem comes from "Applied Statistics and Probability for > > Engineers", 2nd Edition, by D. C. Montgomery. Page736, problem > 14.7. The > > problem is to compare the sample data with a population median of > 8.5. The > > book answer is p = 0.25, wilcox.test answer is p = 0.573. > > I've tried several other similar problems with similar results. I've > copied > > the following directly from my workspace. > > wilcox.exact (from exactRankTests) gives > > > wilcox.exact(x - 8.5) > > Exact Wilcoxon signed rank test > > data: x - 8.5 > V = 80.5, p-value = 0.5748 > > so I'd suspect the textbook. One-sided p-value perhaps? or table > limitation (as in "p > .25"). If you want to dig deeper, you'll probably > have to check the computations implied by the text. > > > Thanks for any help, > > CHV > >> x<-c(8.32,8.05, > >> > 8.93,8.65,8.25,8.46,8.52,8.35,8.36,8.41,8.42,8.30,8.71,8.75,8.6,8.83,8.5,8 38,8.29,8.46) > >> wilcox.test(x,y=NULL,mu=8.5) > > Wilcoxon signed rank test with continuity correction > > data: x > > V = 80.5, p-value = 0.573 > > alternative hypothesis: true location is not equal to 8.5 > > > > Warning messages: > > 1: In wilcox.test.default(x, y = NULL, mu = 8.5) : > > cannot compute exact p-value with ties > > 2: In wilcox.test.default(x, y = NULL, mu = 8.5) : > > cannot compute exact p-value with zeroes > >   > > Charles H Van deZande > > > > > > > > > > > >  > > > -- > O__ ---- Peter Dalgaard Ãster Farimagsgade 5, Entr.B > c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K > (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 > ~~~~~~~~~~ - (p.dalga...@biostat.ku.dk > <mailto:p.dalga...@biostat.ku.dk>) FAX: (+45) 35327907 > > -- O__ ---- Peter Dalgaard Ãster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalga...@biostat.ku.dk) FAX: (+45) 35327907 [[alternative HTML version deleted]]
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