Dear all, When we perform a Wilcoxon rank sum test (on two samples with different sizes) we get a test statistic. My question is, as the value of test statistic increases the difference between the distributions of the two samples also increase, right? Thanks in advance, João Fadista [[alternative HTML version deleted]]
Jo?o Fadista wrote:> Dear all, > > When we perform a Wilcoxon rank sum test (on two samples with different sizes) we get a test statistic. My question is, as the value of test statistic increases the difference between the distributions of the two samples also increase, right? >Wrong. It has a minimum value of zero and some maximum which increases with the sample size. Both extremes occur for nonoverlapping distributions, whereas the "middle" values correspond to similar distributions. -- O__ ---- Peter Dalgaard ?ster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
On Wed, 17 Oct 2007, [iso-8859-1] Jo?o Fadista wrote:> When we perform a Wilcoxon rank sum test (on two samples with different sizes) > we get a test statistic. My question is, as the value of test statistic > increases the difference between the distributions of the two samples also > increase, right?Depending on how accurate you want to be, the answer is "No" or "Yes" or "No". - No, the test statistic that R reports depends on the sample size: if you take samples twice as large from the same distributions the test statistic will become about four times larger. - Yes, for fixed sample size a larger test statistic indicates a larger difference - No, the test statistic (even standardized for sample size) does not correspond to a well-behaved distance between distributions. For example wilcox.test(x,y) and wilcox.test(y,z) can both be small but wilcox.test(x,z) be large. -thomas Thomas Lumley Assoc. Professor, Biostatistics tlumley at u.washington.edu University of Washington, Seattle