that at this threshold, the test is equally accurate with examinees who are deceptive and those who are nondeceptive. With a threshold set at that point, 72.5 percent of the deceptive examinees and 72.5 percent of the nondeceptive examinees would (on average) be correctly identified in a population with any proportion of examinees who are being deceptive. (For the curves shown in Figure 2-3 with A = 0.9 and A = 0.7, the corresponding balanced thresholds achieve 81.8 and 66.0 percent correct identifications, respectively.) Points F and S in Figure 2-2 represent two other possible thresholds. At point F (for friendly), few are called deceptive: only 12 percent of those who are nondeceptive and 50 percent of those truly deceptive. At point S (for suspicious), many more people are called deceptive: the test catches 88 percent of the examinees who are being deceptive, but at the cost of falsely implicating 50 percent of those who are not.9
Decision theory specifies that a rational diagnostician faced with a set of judgment calls will adopt a threshold or cutoff point for making the diagnostic decisions that minimizes the net costs of false positive and false negative decisions. If all benefits and costs could be measured and expressed in the same units, then this optimal threshold could be calculated for any ROC curve and base rate of target subjects (e.g., cases of deception) in the population being tested (see Chapter 6 and Appendix J for details). A goal of being correct when the positive outcome occurs (e.g., catching spies) suggests a suspicious cutoff like S; a goal of being correct when a negative outcome occurs (avoiding false alarms) suggests a friendly cutoff point like F.
The optimum decision threshold also depends on the probability, or base rate, of the target condition in the population or in the sample at hand—for security screening, this might refer to the proportion of spies or terrorists or potential spies or terrorists among those being screened. Because the costs depend on the number of deceptive individuals missed and the number of nondeceptive individuals falsely implicated (not just on the proportions), wanting to reduce the costs of errors implies that one should set a suspicious cutoff like S when the base rate is high and a friendly cutoff like F when the base rate is low. With a low base rate, such as 1 in 1,000, almost all the errors will occur with truly negative cases (that is, they will be false positives). These errors are greatly reduced in number by using a friendly cutoff that calls fewer test results positive. With a high base rate, such as 8 in 10, most of the errors are likely to be false negatives, and these are reduced by setting a suspicious threshold. Thus, it makes sense to make a positive decision fairly frequently in a referral or