Decision Making Under Uncertainty

Theoretical Basis: Signal Detection Theory

The theoretical basis for obtaining estimates of the decision maker's sensitivity and response bias is known as signal detection theory (SDT). SDT was developed and introduced into psychological research in the 1950s and is a direct application of statistical hypothesis testing to the tasks of detecting “signals” in noisy stimuli and of discriminating between two confusable stimuli. As in statistical hypothesis testing, there are two distributions, the noise-alone (analogous to the null) distribution and the signal + noise (alternative) distribution (see Figure 1). In SDT, the two distributions represent the probabilities of the various strength of evidence that the decision maker has for each of the two possible situations. The two distributions overlap, and there is one point, the decision criterion, along the evidence–strength axis that represents the decision maker's critical decision point for his or her decision rule. The rule applies on each trial and is stated thus: If the evidence received is stronger than the decision criterion, then respond “signal”; if the evidence is weaker, then respond “noise.” The evidence, however, can come from either of the two situations. So, if the strength of evidence falls above the criterion but was from the noise stimulus, fn distribution, then the decision maker has made an error of the false positive type (a false alarm). Alternatively, if it had in fact been from the signal distribution, fs, then the decision maker's response was correct and is referred to as a hit. The areas under the two curves to the right of the criterion are estimated by the proportions of P(hit) and P(false alarm) in Table 1.

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