[R] wilcox.test test statistic

Thomas Lumley tlumley at u.washington.edu
Wed Oct 17 17:35:07 CEST 2007

On Wed, 17 Oct 2007, [iso-8859-1] João 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 Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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