On Fri, May 7, 2010 at 9:45 PM, cheba meier <cheba.me...@googlemail.com>wrote:
> Hi all, > > Thank you for your reply. > > if done properly! What does this mean? The R-code I have is using the > R-function sample without replacement. Am I doing this properly? > > median of the differences is zero! This is only valid if the experiment consists of paired data. > Does this mean if I run 1000 permutation and for each permutation I compute > the median difference and as a result I have 1000 differences. Is the the > H0: median(1000 differences) =0? If yes, which conclusion one would have > from this H0? > Nope. the H0 is : median difference = 0 permutation tests run with replacement=F, bootstrapping (which is arguably the better choice if you can't calculate all permutations) is done with replacement = T # make some data a <- 1:10 b <- 3:12 x <- c(a,b) y <- rep(c("a","b"),each=10) # define function difference of the medians. This can be any function, this is just for demonstration purposes med.diff <-function(x,y){ tmp <- by(x,y,median) return(diff(tmp)) } # bootstrap med.diff.observed <- med.diff(x,y) # observed test statistic n <- 100 # number of bootstraps boot.samples <- replicate(n,sample(x,replace=T)) # bootstrap samples med.diff.boot <- apply(boot.samples,2,med.diff,y) # test statistic for bootstrap samples med.diff.boot <- scale(med.diff.boot) # centralization for 2-sided testing pvalue <- mean(abs(med.diff.boot)>=abs(med.diff.observed)) # calculate proportion of test statistic that is more extreme than the observed pvalue I use the central limit theorem in a way, assuming the distribution of the statistic for the bootstrap sample is symmetric. > Best wishes, > Cheba > > > > 2010/5/7 Joris Meys <jorism...@gmail.com> > > depends on how you interprete "absolute median difference". Is that the >> absolute difference of the medians, or the median of the absolute >> differences. Probably the latter one, so you would be right. If it's the >> former one, then it is testing whether the difference of the medians is >> zero. >> >> Cheers >> Joris >> >> >> On Fri, May 7, 2010 at 6:52 PM, Thomas Lumley >> <tlum...@u.washington.edu>wrote: >> >>> On Fri, 7 May 2010, cheba meier wrote: >>> >>> Dear Thomas, >>>> >>>> I have been running simulations in order me to understand this problem! >>>> I >>>> have found something online where the absolute median difference is >>>> computed >>>> and permutations are ran to compute a p-value. Is such a test (if I can >>>> call >>>> it a test) tests the null hypothesis that median group 1 = median group >>>> 2? >>>> >>> >>> No, that is testing whether the median of the differences is zero. This >>> is not the same as testing whether the difference of the medians is zero. >>> >>> -thomas >>> >>> >>> >>> Thank you in advance for your help. >>>> >>>> Regards, >>>> Cheba >>>> >>>> 2010/4/6 Thomas Lumley <tlum...@u.washington.edu> >>>> >>>> >>>>> >>>>> None of them. >>>>> >>>>> - mood.test() looks promising until you read the help page and see >>>>> that it >>>>> does not do Mood's test for equality of quantiles, it does Mood's test >>>>> for >>>>> equality of scale parameters. >>>>> - wilcox.test() is not a test for equal medians >>>>> - ks.test() is not a test for equal medians. >>>>> >>>>> >>>>> Mood's test for the median involves dichotomizing the data at the >>>>> pooled >>>>> median and then doing Fisher's exact test to see if the binary variable >>>>> has >>>>> the same mean in the two samples. >>>>> >>>>> median.test<-function(x,y){ >>>>> z<-c(x,y) >>>>> g <- rep(1:2, c(length(x),length(y))) >>>>> m<-median(z) >>>>> fisher.test(z<m,g)$p.value >>>>> } >>>>> >>>>> Like most exact tests, it is quite conservative at small sample sizes. >>>>> >>>>> -thomas >>>>> >>>>> >>>>> On Tue, 6 Apr 2010, cheba meier wrote: >>>>> >>>>> Dear all, >>>>> >>>>>> >>>>>> What is the right test to test whether the median of two groups are >>>>>> statistically significant? Is it the wilcox.test, mood.test or the >>>>>> ks.test? >>>>>> In the text book I have got there is explanation for the Wilcoxon >>>>>> (Mann >>>>>> Whitney) test which tests ob the two variable are from the same >>>>>> population >>>>>> and also ks.test! >>>>>> >>>>>> Regards, >>>>>> Cheba >>>>>> >>>>>> [[alternative HTML version deleted]] >>>>>> >>>>>> ______________________________________________ >>>>>> 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. >>>>>> >>>>>> >>>>>> Thomas Lumley Assoc. Professor, Biostatistics >>>>> tlum...@u.washington.edu University of Washington, Seattle >>>>> >>>>> >>>>> >>>> [[alternative HTML version deleted]] >>>> >>>> ______________________________________________ >>>> 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. >>>> >>>> >>> Thomas Lumley Assoc. Professor, Biostatistics >>> tlum...@u.washington.edu University of Washington, Seattle >>> >>> ______________________________________________ >>> 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. >>> >> >> >> >> -- >> Joris Meys >> Statistical Consultant >> >> Ghent University >> Faculty of Bioscience Engineering >> Department of Applied mathematics, biometrics and process control >> >> Coupure Links 653 >> B-9000 Gent >> >> tel : +32 9 264 59 87 >> joris.m...@ugent.be >> ------------------------------- >> Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php >> > > -- Joris Meys Statistical Consultant Ghent University Faculty of Bioscience Engineering Department of Applied mathematics, biometrics and process control Coupure Links 653 B-9000 Gent tel : +32 9 264 59 87 joris.m...@ugent.be ------------------------------- Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php [[alternative HTML version deleted]] ______________________________________________ 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.