On May 4, 2011, at 15:11 , JP wrote: > 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)
You probably don't want the bonferroni correction there. Rather p.adj="none". You generally correct the p values for multiple testing, not the test statistics. (My sentiment would be to pick apart the stats:::wilcox.test.default function and clone the computation of Z from it, but presumably backtracking from the p value is a useful expedient.) > # 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$p.value / 2) > Hmm, you're not actually getting a signed z out of this, you might want to try alternative="greater" and drop the division by 2 inside qnorm(). (If the signs come out inverted, I meant "less" not "greater"...) > > > On 4 May 2011 13:25, peter dalgaard <pda...@gmail.com> wrote: >> >> On May 4, 2011, at 11:03 , JP wrote: >> >>> On 3 May 2011 20:50, peter dalgaard <pda...@gmail.com> wrote: >>>> >>>> On Apr 28, 2011, at 15:18 , JP wrote: >>>> >>>>> >>>>> >>>>> I have found that when doing a wilcoxon signed ranked test you should >>>>> report: >>>>> >>>>> - The median value (and not the mean or sd, presumably because of the >>>>> underlying potential non normal distribution) >>>>> - The Z score (or value) >>>>> - r >>>>> - p value >>>>> >>>> >>>> ...printed on 40g/m^2 acid free paper with a pencil of 3B softness? >>>> >>>> Seriously, with nonparametrics, the p value is the only thing of real >>>> interest, the other stuff is just attempting to check on authors doing >>>> their calculations properly. The median difference is of some interest, >>>> but it is not actually what is being tested, and in heavily tied data, it >>>> could even be zero with a highly significant p-value. The Z score can in >>>> principle be extracted from the p value (qnorm(p/2), basically) but it's >>>> obviously unstable in the extreme cases. What is r? The correlation? >>>> Pearson, not Spearman? >>>> >>> >>> Thanks for this Peter - a couple of more questions: >>> >>> a <- rnorm(500) >>> b <- runif(500, min=0, max=1) >>> x <- wilcox.test(a, b, alternative="two.sided", exact=T, paired=T) >>> x$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 >> >> >> -- 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.
