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 Øster 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 Øster 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
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