Operating Characteristics and a Priori Probability of the Signal

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Abstract
Two fixed-interval observation experiments were conducted to determine the effect of a priori probability of signal occurrence [p(SN)] on signal detectability. The signal was a “pure tone” of 1000 cps, presented for 250 msec against a continuous background of white gaussian noise. (1) Three values of p(SN) (0.25, 0.50, and 0.75) were paired with each of three values of E/N0 (6.3, 12.6, and 20.0). (2) With E/N0 fixed at 12.6, p(SN) was assigned values of 0.10, 0.25, 0.50, 0.75, and 0.90. Listeners employed a four-point rating scale to indicate their confidence that a signal had been presented. Operating characteristics were fitted to the data on normal probability paper. An obtained operating characteristic indicates the detectability of the signal for the listener and may be specified completely by its two parameters, slope and √de. The results indicate that √de is independent of p(SN), as predicted by the Theory of Signal Detectability. The slope of the operating characteristic, on the other hand, appears to be a joint function of p(SN) and E/N0. With E/N0 = 20.0, slope increased markedly as p(SN) increased; with E/N0 = 12.6, slope was a nondecreasing function of p(SN), ranging from about 0.70 for p(SN) = 0.10 to about 1.00 for p(SN) = 0.90; and with E/N0 = 6.3, slope was independent of p(SN). (This research was supported by the Operational Applications Laboratory, Air Force Cambridge Research Center.)

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