The computation of the standard error for AUC is not trivial. Its computation, and comparisons among AUCs, is detailed in the DeLong, DeLong, and Clarke-Pearson reference cited in the "Details/Receiver Operating Characteristic Curves/Comparing ROC Curves" and "References" section of the LOGISTIC documentation.
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ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.