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Signal detection theory: The receiver operating characteristic

Part 1 of this posting discussed the problem of trying to tell whether or not a signal is being received, despite the confounding influence of additive noise in the measurement process. As we saw, distributions of noise measurements and distributions of signal-plus-noise measurements may show substantial overlap. This can make it impossible to always judge correctly whether a signal is present or absent.

A measurement cutoff or criterion may be used to judge a measurement (see figure below). Above this criterion, some judgments will be true positives (also called hits or detections), while some will be false positives (also called false alarms). Below the criterion, some judgments will be false negatives (also called misses), and some measurements will be true negatives (also called correct rejections). These correct and incorrect judgments of noise vs. signal-plus-noise can be arranged in a two-by-two grid of signal detection outcomes called a confusion matrix.

The judgment criterion may be smoothly raised and lowered, causing the proportion of measurements in each outcome to change. The results may be summarized in a plot called a receiver operating characteristic or ROC curve (pronounced "R-O-C," or sometimes "rock"). Lowering the criterion errs on the side of more true positives, whereas raising the criterion errs on the side of fewer false positives. More value or risk might be associated with one or another of these, depending on the job at hand.

Efforts may be made to decrease the strength of the noise, and/or to increase the strength of the signal, so that there is less overlap between distributions. The sensitivity of a signal detection task measures how well-separated the two distributions are. Highly overlapping distributions will result in more judgment errors, in which case the sensitivity is low. Minimally overlapping distributions will increase sensitivity and result in more area under the ROC curve, reflecting an improved receiver operating characteristic and an easier detection task.

The author's affiliation with The MITRE Corporation is provided for identification purposes only, and is not intended to convey or imply MITRE's concurrence with, or support for, the positions, opinions, or viewpoints expressed by the author.

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