Figure 2.2. Two examples showing how receiver operating characteristic (ROC) curves are derived from noxious and tasty beetle distributions. (A) When the two overlapping distributions are well separated, the receiver operating characteristic (ROC) is bowed toward the ideal [P(FA) = 0, P(CA) = 1] point. (B) When the two distributions are close together, the curve is less bowed out and more linear.
operating characteristic curve. Part B shows a more difficult discrimination problem in which the two distributions overlap more, so that a forager finds it difficult to reject noxious beetles without also rejecting tasty ones. This situation leads to a much flatter receiver operating characteristic curve. In the limiting case, in which the two distributions are exactly the same (complete overlap), the receiver operating characteristic curve would be a straight line connecting (0,0) and (1,1). The extent to which the receiver operating characteristic curve bows out away from linearity is, therefore, a measure of the "discriminability" of the situation.
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