# ROC analysis: AUC tests in SPSS and Stata

When SPSS tests the AUC of a ROC curve against the chance area (0.5), which statistical test does it use for this? And what are its motivations to use it? This seems to be documented nowhere.

Because SPSS does not allow AUC comparison, I use Stata to do this.

In Stata, it is explained that a chi2 test is used to compare AUCs (using roccomp). But what is the motivation for this? What would the contingency table look like?

EDIT: In IBM SPSS Statistics 24 Algorithms I found the following. Does this mean SPSS uses a Z-test? (W = AUC)

• This seems to be documented nowhere Really? Did you consider SPSS Statistics Algorithms document? – ttnphns Aug 8 '17 at 7:02
• There it gives a complex formula for the p-value without stating the type of test (e.g. t-test, wilcoxon,...). My stat. knowledge is too limited to interpret that. – Zxifer Aug 8 '17 at 8:11
• Not sure how to do that in SPSS but the test $H_0$=0.5 can be easily done by SAS using proc freq and a binomial option. – Deep North Aug 8 '17 at 23:24