Decision Processes of Same-Different Judgements for the Amplitude Discrimination of Single Sinusoids and Auditory Profile Complexes

Abstract

Two detection-theoretic models have been developed to account for an observer's decision process when judging whether two similar stimuli are the same or different. One model, the differencing model, supposes the observer computes the difference between the effects of the two stimuli; the other model, the independent-observation model, supposes in its simplest form that the observer categorizes each stimulus separately and compares the categories. The two models yield discrepant estimates of an observer's ability to distinguish between the stimuli, measured by the index d'. Therefore, in order to obtain a valid measure of discriminability from same-different judgements, the proper model of the decision process must first be determined. Three methods were employed for this purpose: (1) analysis of the shape of the Receiver Operating Characteristic (ROC); (2) decision-space analysis; and (3) a correlation method. Of these methods, analysis of the shape of the ROC was found to be susceptible to violations of two assumptions: that the observer's decision criteria were stable, and that the judgements were symmetric, that is, that they were independent of the order in which the stimuli occurred. Decision-space analysis proved to be more robust to violations of these assumptions than the other methods. When these assumptions were not met, decision-space analysis and the correlation method could supplement ROC analysis. To investigate the models experimentally, same-different judgements about two types of auditory stimuli were investigated. These were simple l-kHz sinusoidal waveforms, and complex waveforms comprising 11 sinusoidal components. In order to discount the effects of an observer's internal noise, the amplitude of the stimuli was randomised from presentation to presentation by Gaussian perturbations. Two experiments investigated the ability of observers to distinguish between two sets of simple l-kHz sinusoids drawn from Gaussian distributions with different mean amplitudes. The sinusoids were presented in pairs, in which members of the pair could be drawn from the same or different distributions. An observer decided whether the two sinusoids came from the same or different distributions. The differencing model provided a better account of these judgements than the independent-observations model, even when the observers were encouraged to make independent-observation judgements. Four further experiments investigated the discriminability of two classes of complex stimuli for which the central frequency component could differ in amplitude from the other components. The variance of the Gaussian perturbations was found to be crucial to an observer's ability to discriminate between stimuli of this type. Moreover, the independent-observation model provided a better account of this task, which is known as profile analysis. The discriminability of each kind of stimulus, simple or complex, could thus be estimated from the appropriate decision model. Even though the physical difference between the simple sinusoids was the same as the physical difference between the complex sounds (a difference in amplitude of a single sinusoid), the decision processes adopted to distinguish between them were different. It was inferred that the auditory attribute, which serves as the basis for same-different judgements, differs for simple and complex sounds. For simple sounds it was inferred that the observer judged them to be the same or different by computing their difference in loudness, whereas for complex sounds it was inferred that the observer categorized each sound separately on the basis of its timbre or auditory qualify.