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medians in Wilcoxon disagree with median function
5 messages · Graham Smith, Brian Ripley, David Winsemius
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Where did you get the idea that the location estimate in a 2-sample Wilcoxon test is the difference in medians? (It is a common misconception, but not I believe to be found in R. The estimate is the median of differences, not the difference of medians: and the test is not of a difference of population medians either, unless the two populations differ only in location.)
On Sun, 30 Jan 2011, Graham Smith wrote:
I am sure I am opening myself up to looking stupid, but I have two samples with medians of 613.5 and 189 (difference in location of 424 compared to the difference suggested from the wilcoxon of 291.5)
wilcox.test(pipwtCount,pipwdCount, conf.int=TRUE, na.rm=TRUE)
Wilcoxon rank sum test
data: pipwtCount and pipwdCount
W = 822, p-value = 0.01227
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
58 639
sample estimates:
difference in location
291.5
The data is here
pipwtCount
[1] 532 298 215 1588 38 180 284 376 5349 1024 650 605 1307 6147 21 [16] 453 23 1983 1048 464 2183 1028 1361 163 175 5944 569 622 793 70 [31] 67 1188 248 3010 19 2179 1339 408 113 739 2615 4619
pipwdCount
[1] 89 384 12 703 2 138 189 383 314 482 96 907 90 1193 154 [16] 305 61 414 4764 1066 121 143 102 174 44 2896 NA 1103 161 199
median(pipwtCount)
[1] 613.5
median(pipwdCount,na.rm=T)
[1] 189
613.5-189
[1] 424.5 I would appreciate if someone could point out the obvious to me, and explain why there is such a large discrepancy in the differences in location. Many thanks, Graham [[alternative HTML version deleted]]
______________________________________________ R-help at 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.
Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595
On Jan 30, 2011, at 9:28 AM, Graham Smith wrote:
I am sure I am opening myself up to looking stupid,
Or exposing a failure to read the help page.
but I have two samples with medians of 613.5 and 189 (difference in location of 424 compared to the difference suggested from the wilcoxon of 291.5)
wilcox.test(pipwtCount,pipwdCount, conf.int=TRUE, na.rm=TRUE)
Wilcoxon rank sum test
data: pipwtCount and pipwdCount
W = 822, p-value = 0.01227
alternative hypothesis: true location shift is not equal to 0
95 percent confidence interval:
58 639
sample estimates:
difference in location
291.5
The Wilcoxon two sample test is not a test of equality of medians. Read the Details help page. The estimated location is a pseudomedian. > plot(density(pipwtCount)) > plot(density(pipwdCount, na.rm=TRUE)) Both are highly right-skewed.
David. > The data is here > >> pipwtCount > [1] 532 298 215 1588 38 180 284 376 5349 1024 650 605 1307 > 6147 > 21 > [16] 453 23 1983 1048 464 2183 1028 1361 163 175 5944 569 > 622 793 > 70 > [31] 67 1188 248 3010 19 2179 1339 408 113 739 2615 4619 > >> pipwdCount > [1] 89 384 12 703 2 138 189 383 314 482 96 907 90 > 1193 > 154 > [16] 305 61 414 4764 1066 121 143 102 174 44 2896 NA > 1103 161 > 199 > >> median(pipwtCount) > [1] 613.5 >> median(pipwdCount,na.rm=T) > [1] 189 >> 613.5-189 > [1] 424.5 > > > I would appreciate if someone could point out the obvious to me, and > explain > why there is such a large discrepancy in the differences in location. > > > > Many thanks, > > Graham > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at 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. David Winsemius, MD West Hartford, CT
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