Proportion of Correct Responses as a Function of the Number of Stimulus-Response Alternatives

Abstract

The effect of the number of stimulus-response alternatives on the human observer's probability of making a correct response was predicted by three models: a simple threshold model; the constant-ratio rule with simplifying assumptions; and the theory of signal detectability with simplifying assumptions. Four types of signal ensembles were used in these experiments: (a) speech signals; (b) a sinusoidal signal occurring in one of n intervals in time; (c) sinusoidal signals of varying amplitude; and (d) sinusoidal signals of varying frequency. In all of these experiments the listeners had complete knowledge of the set of stimuli under test and limited their responses accordingly. The simple threshold model failed to account for any of the data. The simplified version of the constant-ratio rule and the simplified version of the theory of signal detectability were both compatible with the data obtained in the speech experiments. Also, over the small range tested, both handled data obtained when a sinusoidal signal occurred in one of n intervals. No model tested was sufficiently complex to account for data when the sinusoidal signals varied only in amplitude or only in frequency. (Work under sponsorship of Operational Applications Laboratory, Air Force Cambridge Research Center, and U. S. Army, Signal Corps Engineering Laboratories, Fort Monmouth.)