On May 4, 2011, at 11:03 , JP wrote: > On 3 May 2011 20:50, peter dalgaard <pda...@gmail.com> wrote: >> >> On Apr 28, 2011, at 15:18 , JP wrote: >> >>> >>> >>> I have found that when doing a wilcoxon signed ranked test you should >>> report: >>> >>> - The median value (and not the mean or sd, presumably because of the >>> underlying potential non normal distribution) >>> - The Z score (or value) >>> - r >>> - p value >>> >> >> ...printed on 40g/m^2 acid free paper with a pencil of 3B softness? >> >> Seriously, with nonparametrics, the p value is the only thing of real >> interest, the other stuff is just attempting to check on authors doing their >> calculations properly. The median difference is of some interest, but it is >> not actually what is being tested, and in heavily tied data, it could even >> be zero with a highly significant p-value. The Z score can in principle be >> extracted from the p value (qnorm(p/2), basically) but it's obviously >> unstable in the extreme cases. What is r? The correlation? Pearson, not >> Spearman? >> > > Thanks for this Peter - a couple of more questions: > > a <- rnorm(500) > b <- runif(500, min=0, max=1) > x <- wilcox.test(a, b, alternative="two.sided", exact=T, paired=T) > x$statistic > > V > 31835 > > What is V? (is that the value Z of the test statistic)?
No. It's the sum of the positive ranks: r <- rank(abs(x)) STATISTIC <- sum(r[x > 0]) names(STATISTIC) <- "V" (where x is actually x-y in the paired case) Subtract the expected value of V (sum(1:500)/2 == 62625) in your case, and divide by the standard deviation (sqrt(500*501*1001/24)=3232.327) and you get Z=-9.54. The slight discrepancy is likely due to your use of exact=T (so your p value is not actually computed from Z). > > z.score <- qnorm(x$p.value/2) > [1] -9.805352 > > But what does this zscore show in practice? That your test statistic is approx. 10 standard deviations away from its mean, if the null hypothesis were to be true. > > The d.f. are suggested to be reported here: > http://staff.bath.ac.uk/pssiw/stats2/page2/page3/page3.html > Some software replaces the asymptotic normal distribution of the rank sums with the t-distribution with the same df as would be used in an ordinary t test. However, since there is no such thing as an independent variance estimate in the Wilcoxon test, it is hard to see how that should be an improvement. I have it down to "coding by non-statistician". > And r is mentioned here > http://huberb.people.cofc.edu/Guide/Reporting_Statistics%20in%20Psychology.pdfs > > Aha, so it's supposed to be the effect size. On the referenced site they suggest to use r=Z/sqrt(N). (They even do so for the independent samples version, which looks wrong to me). > >>> My questions are: >>> >>> - Are the above enough/correct values to report (some places even >>> quote W and df) ? >> >> df is silly, and/or blatantly wrong... >> >>> What else would you suggest? >>> - How do I calculate the Z score and r for the above example? >>> - How do I get each statistic from the pairwise.wilcox.test call? >>> >>> Many Thanks >>> JP >>> >>> ______________________________________________ >>> R-help@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. >> >> -- >> Peter Dalgaard >> Center for Statistics, Copenhagen Business School >> Solbjerg Plads 3, 2000 Frederiksberg, Denmark >> Phone: (+45)38153501 >> Email: pd....@cbs.dk Priv: pda...@gmail.com >> >> -- Peter Dalgaard Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@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.