[R] AUC, C-index and p-value of Wilcoxon

Petr Savicky savicky at cs.cas.cz
Thu Feb 9 18:33:09 CET 2012

On Thu, Feb 09, 2012 at 02:05:08PM +0000, linda Porz wrote:
> Dear all,
> I am using the ROCR library to compute the AUC and also the Hmisc library
> to compute the C-index of a predictor and a group variable. The results of
> AUC and C-index are similar and give a value of about 0.57. The Wilcoxon
> p-value is <0.001! Why the AUC is showing small value and the p-value is
> high significant? The AUC is based on Wilcoxon calculation?


There is no direct relationship between AUC and p-value of 
Wilcoxon. AUC measures, how well two distributions may be
separated. The p-value measures, to which extent it is
clear that the distributions are different. The test is
significant, even if it is very clear that there is a tiny
difference between the two distributions. This may happen
for a large sample size. If the sample size increases,
then AUC for separating variables X, Y converges to P(X < Y),
which may be 0.57 and still, the p-value may converge to 0.

Hope this helps.

Can you send a concrete numerical example?

Petr Savicky.

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