On Sequential Decisions by Human Observers in a Signal Detection Problem

Abstract

In a sequential test of statistical hypotheses, a sample is taken, and one of three decisions is made: accept H0, accept H1, or take another sample. Samples are taken successively until the resulting sequence of samples is sufficiently persuading in favor of one or the other terminal decision. The criteria which are to be met before making a terminal decision are stated in terms of the error probabilities that lead to maximizing the expected value of a decision. These error probabilities, and hence the average number of samples preceding a terminal decision, are functions of the a priori probabilities of H0 and H1, the values associated with the four possible outcomes of a terminal decision, the cost of taking a sample, and the divergence between the distributions of sample values expected under H0 and under H1. The optimum sequential test generally requires less time on the average than a test of fixed length that yields the same error probabilities. This paper deals with an experimental application of the theory of sequential testing to the human observer making decisions concerning the presence of signals in noise. Our observers made as many observations as they chose before asserting the existence of noise alone or of signal plus noise. They knew, in each of several experiments which varied in these respects, the values of the situational parameters that ideally govern the choice of the decision criteria. Their performance is compared to optimum performance in terms of error probabilities and average number of observations. A comparison is also made of their relative efficiency in sequential tests and tests of fixed length. [This study was supported by the Operational Applications Laboratory of the Cambridge Research Center under Contract AF19(604)-1728.]