3

Why is the area under the curve measure better than the accuracy ratio?

I know that the AR lies between 0,5 and 1 and the relationship $AUC=\frac{1}{2}(AR+1)$ holds, so the AUC lies between 0,75 and 1, but this does not really seem to be an advantage.

jonsca
  • 1,772
testify
  • 31
  • AUC should be between 0.5 and 1. It can actually take any value in [0, 1], but values below 0.5 indicate that you could get a better classifier by inverting class labels. – cbeleites unhappy with SX Feb 13 '13 at 15:20

1 Answers1

5

ROC curves are useful because they reveal how the classifier trades between false positives and false negatives. This is generally useful, but can be particularly handy when dealing with very unbalanced class distributions.

For example, about 1 in 200 people in the US have HIV/AIDS. I could design a dirt cheap test that is 99.5% accurate: I'll just say no one has it! Even though this test is clearly worthless (and reprehensible!), it has a very high accuracy. However, the shape of the ROC would reveal that this test is lousy!

You're correct that the AUC, by itself, is not the be-all and end-all of classifier evaluation, but I'd argue that examining the curve itself is an important step and reporting the AUC is a decent way of summarizing that.

Matt Krause
  • 21,095