What does the Kolmogorov-Smirnov (KS) statistic describe?

The Kolmogorov-Smirnov (KS) statistic is a crucial measure in statistical modeling, particularly in the context of evaluating predictive models. It is used to determine how well a model can distinguish between different outcomes, such as predicting binary events. The KS statistic quantifies the maximum distance between the empirical cumulative distribution functions (CDFs) of the predicted probabilities for the positive class versus the negative class.

A higher KS statistic indicates better separation between the two distributions, suggesting that the model is effective at distinguishing between the outcomes. Essentially, it assesses the model's ability to identify positives vs. negatives based on the predicted scores, making it a valuable tool for measuring model performance, especially in fields like credit scoring or risk assessment.

The other options do not accurately capture the primary purpose of the KS statistic. While the percent of concordant cases pertains to rank ordering, and error in prediction relates to general accuracy measures, the KS statistic specifically focuses on the separation of outcomes rather than merely counting cases or quantifying modeling data.