a. All ROCs connect the lower left corner where the hit and false alarm rates of both zero, with the upper right corner where hit and false alarm rates are both 1.00. When d' = 0, the ROC is a straight line from the lower left to the upper right. This is because the signal and noise distributions overlap perfectly, and so the hit and false alarm rates are equal to each other at every criterion. If we reduce criterion in an effort to increase hits, we find that false alarms increase exactly as much as the hits. When d' = 3, the hit rates rise much more quickly than false alarm rates as the criterion moves toward the left from the extreme right. Thus, the ROC curve rises very quickly toward the top left corner. As the criterion becomes more liberal (smaller, to the left), the false alarm rates begin to increase. When the criterion crosses the intersection of the two normal curves, the false alarm rate rises more quickly than the hit rate. With greater sensitivity, the ROC is higher and to the left. Sensitivity can also be measured by the area between the ROC and the diagonal line. This area is larger when d' is larger, and it is zero when d' is zero.
b. Anita and Bob each generate one point on the same ROC. They have the same ROC, and thus the same d' value.
c. For Chris, d' = 2.62 and criterion = 1.34. Thus, Chris has the same criterion as Bob. However, Chris is more sensitive than Bob, as reflected by the larger d' and the more convex ROC.
