Peter thanks for the fantastically simple and understandable explanation...
To sum it up... to find the z values of a number of pairwise wilcox tests do the following: # pairwise tests with bonferroni correction x <- pairwise.wilcox.test(a, b, alternative="two.sided", p.adj="bonferroni", exact=F, paired=T) # what is the data structure we got back is.matrix(x$p.value) # p vals x$p.value # z.scores for each z.score <- qnorm(x$p.value / 2) On 4 May 2011 13:25, peter dalgaard <pda...@gmail.com> wrote: > > On May 4, 2011, at 11:03 , JP wrote: > >> On 3 May 2011 20:50, peter dalgaard <pda...@gmail.com> wrote: >>> >>> On Apr 28, 2011, at 15:18 , JP wrote: >>> >>>> >>>> >>>> I have found that when doing a wilcoxon signed ranked test you should >>>> report: >>>> >>>> - The median value (and not the mean or sd, presumably because of the >>>> underlying potential non normal distribution) >>>> - The Z score (or value) >>>> - r >>>> - p value >>>> >>> >>> ...printed on 40g/m^2 acid free paper with a pencil of 3B softness? >>> >>> Seriously, with nonparametrics, the p value is the only thing of real >>> interest, the other stuff is just attempting to check on authors doing >>> their calculations properly. The median difference is of some interest, but >>> it is not actually what is being tested, and in heavily tied data, it could >>> even be zero with a highly significant p-value. The Z score can in >>> principle be extracted from the p value (qnorm(p/2), basically) but it's >>> obviously unstable in the extreme cases. What is r? The correlation? >>> Pearson, not Spearman? >>> >> >> Thanks for this Peter - a couple of more questions: >> >> a <- rnorm(500) >> b <- runif(500, min=0, max=1) >> x <- wilcox.test(a, b, alternative="two.sided", exact=T, paired=T) >> x$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.
