wilcox.test test statistic

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