# wilcox.test returned estimates

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## wilcox.test returned estimates

 Hi all, I have being using wilcox.test to test for differences between 2 independent samples.  I had understood the difference in location to be conventionally the difference in the sample medians however this is not the case when implemented in R.  I have tied ranks and therefore non-exact p-value and confidence intervals are calculated due to the normal approximation.  But what exactly is this normal approximation i.e. how is it involved in estimating the location difference? Further, is it then wrong to refer to the difference in location as the difference between the medians?  Does anyone have a more appropriate description? Thanks Rebecca ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: wilcox.test returned estimates

 On Wed, 15 Feb 2006, [hidden email] wrote: > Hi all, > > I have being using wilcox.test to test for differences between 2 independent > samples.  I had understood the difference in location to be conventionally the > difference in the sample medians however this is not the case when implemented > in R. I have tied ranks and therefore non-exact p-value and confidence > intervals are calculated due to the normal approximation.  But what exactly is > this normal approximation i.e. how is it involved in estimating the location > difference? the reference distribution is not involved in _estimating_ the difference in location. `wilcox.test' implements the Hodges-Lehmann estimator: from `stats/R/wilcox.test.R'                  ## Exact confidence interval for the location parameter                  ## mean(x) - mean(y) in the two-sample case (cf. the                  ## one-sample case).                  alpha <- 1 - conf.level                  diffs <- sort(outer(x, y, "-"))                  ...                  ESTIMATE <- median(diffs)                  names(ESTIMATE) <- "difference in location" which simply is the median of all pairwise differences. However, the usual normal approximation to the exact conditional distribution (in case of ties) of the Wilcoxon-Mann-Whitney statistic (see Hajek, Sidak, Sen for example) is involved in computing a confidence interval for the difference in location. Hope that helps, Torsten > > Further, is it then wrong to refer to the difference in location as the > difference between the medians?  Does anyone have a more appropriate > description? > > Thanks > > Rebecca > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html> > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: wilcox.test returned estimates

 In reply to this post by pmt1rew On Wed, 15 Feb 2006, [hidden email] wrote: > Hi all, > > I have being using wilcox.test to test for differences between 2 independent > samples.  I had understood the difference in location to be conventionally the > difference in the sample medians however this is not the case when implemented > in R.  I have tied ranks and therefore non-exact p-value and confidence > intervals are calculated due to the normal approximation.  But what exactly is > this normal approximation i.e. how is it involved in estimating the location > difference? It isn't.  The only assumption is that the distribution is the same apart from location in the two groups. > Further, is it then wrong to refer to the difference in location as the > difference between the medians?  Does anyone have a more appropriate > description? Well, this gets more complicated.  Since the method assumes that the population distributions differ only by location the population difference in medians is the same as the difference in means or in 16.34th percentile, or 42%-trimmed mean or whatever. If the assumption is not true then seriously weird things can happen (consider the distributions given by http://mathworld.wolfram.com/EfronsDice.html) However, the estimate is not the difference in sample medians. It is the median pairwise difference.   -thomas Thomas Lumley Assoc. Professor, Biostatistics [hidden email] University of Washington, Seattle ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html