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118 4 Statistical Classification
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Table 4.3. Sensitivity and specificity in impulse detection (100 signal values).

Threshold Sensitivity Specificity

As shown in Table 4.3, there is a compromise to be made between sensitivity
and specificity. This compromise is made more patent in the ROC curve, which
was obtained with the SPSS, and corresponds to eight different threshold values, as
shown in Figure 4.3321. Notice that given the limited number of values the ROC
curve has a stepwise aspect, with different values of the FPR corresponding to the
same sensitivity, as also appearing in Table 4.3 for the specificity value of 0.7.
With a large number of signal samples and threshold values one would obtain a
smooth ROC curve, as represented in Figure 4.33b.

Figure 4.33. ROC curve (bold line) for the Signal Noise data: (a) Eight threshold
values (the values for A=2 and A=3 are indicated); b) A large number of threshold
values (expected curve) with the 45" slope point.

The following characteristic aspects of the ROC curve are clearly visible:

- The ROC curve graphically depicts the compromise between sensitivity and
specificity. If the sensitivity increases, the specificity decreases, and vice-versa.
- All ROC curves start at (0,O) and end at (1,l) (see Exercise 4.16).
- A perfectly discriminating method corresponds to the point (0,l). The ROC
curve is then a horizontal line at a sensitivity =l.