Comparing continuous predictors for a dichotomous variable

Question

I have two continuous predictor variables to predict a dichotomous variable. In addition i have constructed two (interaction) models, based on domain knowledge which use both variables to predict the third.

So now i want to compare these predictors, using R. I get these result on the wilcox test: W = 36655, p-value = 3.896e-09 (single predictor) W = 29680.5, p-value < 2.2e-16 (model)

But i'm wondering if the area under the ROC curve would not be a good (better?) measure then the wilcox or the t-test. To get a general idea of how well the continuous predictor separates the two groups i plot the two histograms together. But the differences are small and besides, i'd like a 'grade' to tell me which is better and by how much.

Answer 1

While the t test and the the Wilcoxon tell you about the statistical significance of the covariate's parameter value, the ROC curve gives a different picture, telling you how well cases are classified as a threshold changes. So from the viewpoint of classification the AUC of the ROC might be more interesting for you.