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The Polygraph and Lie Detection
Appendix I
False Positive Index Values for Polygraph Testing
Table I-1 illustrates the effects of accuracy and thresholds on the false positive index, with four illustrative base rates (the false positive index is the number of false positive test results for each true positive test result). It shows that increasing test accuracy makes for more attractive tradeoffs in using the test. For example, it shows that that for any base rate, if the threshold is set so as to correctly detect 50 percent of truly positive cases, or major security risks (shown in Table I-1B), a diagnostic with A = 0.80 has a false-positive index of about three times that of a diagnostic with A = 0.90; a diagnostic with A = 0.70 has an index of about six times that of a test with A = 0.90; and a diagnostic with A = 0.60 has an index of about eight times that of a test with A = 0.90. These ratios vary somewhat with the threshold selected, but they illustrate how much difference it would make if a high value of A could be achieved for field polygraph testing. If the diagnosis of deception could reach a level of A = 0.90, testing would produce much more attractive tradeoffs between false positives and false negatives than it has at lower levels of A. Nevertheless, if the proportion of major security risks in the population being screened is equal to or less than 1 in 1,000, it is reasonable to expect even with optimistic assessments of polygraph test accuracy that each spy or terrorist that might be correctly identified as deceptive would be accompanied by at least hundreds of nondeceptive examinees mislabeled as deceptive, from whom the spy or terrorist would be indistinguishable by polygraph test result. The possibility that deceptive examinees may use countermeasures makes this tradeoff even less attractive.
Figures I-1 through I-4 enable readers to derive values of the false
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The Polygraph and Lie Detection
TABLE I-1A Values of the False Positive Index with Decision Thresholds Set for 80 Percent Sensitivity
Base rate
A = 0.90
A = 0.80
A = 0.70
A = 0.60
0.001
208
452
634
741
0.01
21
45
63
73
0.10
1.9
4.1
5.7
6.7
0.50
0.21
0.45
0.63
0.74
TABLE I-1B Values of the False Positive Index with Decision Thresholds Set for 50 Percent Sensitivity
Base rate
A = 0.90
A = 0.80
A = 0.70
A = 0.60
0.001
70
232
411
545
0.01
7.0
23
41
54
0.10
0.63
2.1
3.7
4.9
0.50
0.07
0.23
0.41
0.55
TABLE I-1C Values of the False Positive Index with Decision Thresholds Set for 20 Percent Sensitivity
Base rate
A = 0.90
A = 0.80
A = 0.70
A = 0.60
0.001
20
104
240
370
0.01
2.0
10
24
37
0.10
0.18
0.94
2.2
3.3
0.50
0.02
0.10
0.24
0.37
positive index (FPI) from assumptions about the base rate of deceptive examinees in a population to be given polygraph tests, the level of accuracy achieved by the polygraph, and the decision threshold, defined in terms of the sensitivity, or proportion of deceptive individuals to be identified correctly. The figures show values for accuracy rates (A) of 0.90, 0.80, 0.70, and 0.60 and sensitivities of 80, 50, and 20 percent. The figures are based on the binormal, equivariance model and are presented on logarithmic scales to make it easier to get accurate readings for very low base rates than is possible with standard scales such as presented in Figures 7-1 and 7-2.
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The Polygraph and Lie Detection
FIGURE I-1 False positive index values as a function of base rate of deception for a diagnostic procedure with an accuracy index (A) of 0.90 and threshold values achieving sensitivities of 80 percent, 50 percent, and 20 percent.
FIGURE I-2 False positive index values as a function of base rate of deception for a diagnostic procedure with an accuracy index (A) 0.80 and threshold values achieving sensitivities of 80 percent, 50 percent, and 20 percent.
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FIGURE I-4 False positive index values as a function of base rate of deception for a diagnostic procedure with an accuracy index (A) of 0.60 and threshold values achieving sensitivities 80 percent, 50 percent, and 20 percent.
FIGURE I-3 False positive index values as a function of base rate of deception for a diagnostic procedure with an accuracy index (A) of 0.70 and threshold values achieving sensitivities of 80 percent, 50 percent, and 20 percent.
Representative terms from entire chapter:
false positive