# ROC Curves

This procedure is a useful way to evaluate the performance of classification schemes in which there is one variable with two categories by which subjects are classified.

**Example.** It is in a bank's interest to correctly classify customers into those customers who
will and will not default on their loans, so special methods are developed for making these
decisions. ROC curves can be used to evaluate how well these methods perform.

**Statistics.** Area under the ROC curve with confidence interval and coordinate points of the
ROC curve. Plots: ROC curve.

**Methods.** The estimate of the area under the ROC curve can be computed either
nonparametrically or parametrically using a binegative exponential model.

ROC Curve Data Considerations

The old ROC Curve procedure supports the statistical inference about a single ROC curve. This may also be recovered by the new ROC Analysis procedure. Furthermore, the new ROC Analysis procedure can compare two ROC curves generated from either independent groups or paired subjects.

**Data.** Test variables are quantitative. Test variables are often composed of probabilities
from discriminant analysis or logistic regression or composed of scores on an arbitrary scale
indicating a rater's "strength of conviction" that a subject falls into one category or another
category. The state variable can be of any type and indicates the true category to which a subject
belongs. The value of the state variable indicates which category should be considered
*positive*.

**Assumptions.** It is assumed that increasing numbers on the rater scale represent the
increasing belief that the subject belongs to one category, while decreasing numbers on the scale
represent the increasing belief that the subject belongs to the other category. The user must choose
which direction is *positive*. It is also assumed that the *true* category to which each
subject belongs is known.

To Obtain an ROC Curve

This feature requires the Statistics Base option.

- From the menus choose:
- Select one or more test probability variables.
- Select one state variable.
- Identify the
*positive*value for the state variable.

This procedure pastes ROC command syntax.