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ROC curve appears under diagonal reference line

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Question

I produced an ROC (Receiver Operating Characteristic) curve with the ROC command (Analyze>ROC Curve) in IBM SPSS Statistics. My State Variable (STATEVAR) is binary (0,1), with 1 specified as the "Value of State Variable". My Test variable is named TESTVAR. I took the defaults in the Options dialog of the ROC Curve procedure. Here is my syntax command: ROC testvar BY statevar (1) /PLOT=CURVE(REFERENCE) /PRINT=SE COORDINATES /CRITERIA=CUTOFF(INCLUDE) TESTPOS(LARGE) DISTRIBUTION(FREE) CI(95) /MISSING=EXCLUDE. In the graph that was produced, the ROC curve is below the diagonal reference line, projecting into the lower right half of the graph. The Area Under the Curve (AUC) is .260 and significantly different from .5. I expected the ROC curve to be above the reference line, projecting into the upper left half of the graph, with an AUC value above .5. What does it mean when the ROC curve is below the reference line? Can such a curve be interpreted? Does the AUC below .5 mean that the Test Variable is performing worse than chance?

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Modified date:
16 June 2018

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swg21573229