Signal-detection analysis of group decision making.

How effectively can groups of people make yes-or-no decisions? To answer this question, we used signal-detection theory to model the behavior of groups of human participants in a visual detection task. The detection model specifies how performance depends on the group's size, the competence of the members, the correlation among members' judgments, the constraints on member interaction, and the group's decision rule. The model also allows specification of performance efficiency, which is a measure of how closely a group's performance matches the statistically optimal group. The performance of our groups was consistent with the theoretical predictions, but efficiency decreased as group size increased. This result was attributable to a decrease in the effort that members gave to their individual tasks rather than to an inefficiency in combining the information in the members' judgments.

Spreadsheet signal detection.

A number of studies in perception, attention, and memory employ signal detection theory (SDT) to assess the accuracy of an observer's detection or discrimination performance. Some of the problems that students have with understanding and using SDT are associated with the calculations needed to obtain SDT parameters and predictions. All of these calculations, plus the simulation of SDT processes, can be performed using a spreadsheet application program, such as Excel or Quattro Pro. This paper offers a short tutorial on how to use a spreadsheet program to increase your students' knowledge and understanding of SDT.

Effect of temporal position, proportional variance, and proportional duration on decision weights in temporal pattern discrimination.

Two experiments investigated how listeners allocate their attention to different segments of a temporal pattern. The experiments allowed a direct test of the predictions of the Proportion of Total Duration (PTD) rule and the Component Relative Entropy (CoRE) model. Listeners had to decide whether two sequences of nine tones had the same or different temporal patterns (tone duration = 25 ms, tone frequency = 1000 Hz). A sequence's temporal pattern was determined by the time intervals between each tone's offset and the next tone's onset. On same trials, the time intervals at corresponding temporal positions in the two sequences were identical. On different trials, the corresponding time intervals were randomly varied. Listener attention to different temporal positions within a sequence was assessed by calculating the decision weights at each position. The results supported the CoRE model and were inconsistent with the PTD rule. Manipulating the mean of the time intervals within the sequence had no consistent effect on the pattern of weights (or on overall performance), indicating that listener attention was not affected by either the proportion of total duration or the perceptual salience of a longer or shorter time interval. However, manipulating the variance of the time intervals had a significant effect: the highest weight was given to the highest variance segment. This weighting strategy leads to better performance because higher variance segments are more diagnostic of whether the sequences are the same or different.

Effect of sequence delay on the discrimination of temporal patterns.

This experiment tested listeners' ability to discriminate between two temporal patterns as a function of the time interval between the pattern onsets. The listener's task was to decide whether two arrhythmic sequences of nine tones had the same or different temporal patterns; the patterns were defined by the time intervals between the tones. According to the temporal pattern correlation model [R. D. Sorkin, J. Acoust. Soc. Am. 87, 1695-1701 (1990)], listeners extract information about the series of time intervals in each sequence and then compute the correlation between the two series. In the present experiment, the tones in the second sequence were presented at a different frequency than the tones in the first sequence. In one condition, all time intervals in the second sequence were compressed or expanded by a factor that varied randomly over trials. Performance was very good when the sequences did not overlap in time, but was poor when the sequences overlapped. Performance was generally consistent with a discrimination mechanism that cannot process more than one pattern at a time.

Effect of time compression and expansion on the discrimination of tonal patterns.

This experiment tested how well human listeners can discriminate between temporal patterns that are compressed or expanded in time. The listener's task was to determine whether two arrhythmic, tonal sequences had the same or different temporal patterns. According to the pattern correlation model [R. D. Sorkin, J. Acoust. Soc. Am. 87, 1695-1701 (1990)], listeners perform this task by computing the correlation between the pattern of time intervals marked by the tones in each sequence. Listener performance dropped when one of the sequences was compressed or expanded in time. In order for the model to describe the observed performance, it was necessary to postulate an internal noise component that was proportional to the magnitude of the difference between the sequence transformations.

Perception of temporal patterns defined by tonal sequences.

This experiment tested how listeners discriminate between the temporal patterns defined by two sequences of tones. Two arrhythmic sequences of n tones were played successively (n = 8, 12, or 16, tone duration = 35 ms, frequency = 1000 Hz), and the listener reported whether the sequences had the same or different temporal patterns. In the first sequence, the durations of the intertone gaps were chosen at random; in the second sequence, the gaps were either (a) the same as the first sequence or (b) chosen at random. Discrimination performance increased with the variability of the gap sequences and decreased with the size of the correlation between the sequences. A discrimination model based on computation of the sample correlation between the sequences of gaps, but limited by an internal variability of approximately 15 ms, described observer performance in a variety of conditions.

Temporal factors in the discrimination of tonal sequences.

Human observers were asked to judge whether or not two sequences of eight or more tones had the same serial pattern of frequencies. The temporal envelopes of the sequences were manipulated by randomly varying the tone durations or intertone gaps. In the correlated condition, the temporal envelopes of the sequences were varied across trials; the two sequences within each trial had the same temporal envelope. In the uncorrelated condition, the temporal envelopes were varied both across and within trials; every sequence had a unique temporal pattern. Performance in the uncorrelated condition decreased with increased variability in the temporal envelope. Performance in the correlated condition was independent of temporal variability, but decreased with increases in the time interval between the onsets of the two sequences. This pattern of results is consistent with an extension of a model of auditory discrimination developed by Durlach and Braida [J. Acoust. Soc. Am. 46, 372-383 (1969)], in which two processing modes are postulated: a trace mode and a context mode. When the tonal sequences had unique temporal patterns, context mode processing was dominant; when the sequences had identical temporal patterns, trace mode processing was preferred. The effect of variables such as the number of tones, the tone duration, the time gap between tones, and the time interval between sequences was consistent with the predictions of the discrimination model.

Discrimination of temporal jitter in patterned sequences of tones.

The perception of pure tone sequences in highly dependent on the serial pattern of tone frequencies. We propose that this phenomenon is mediated by a frequency-selective mechanism. Three models of the selective mechanism were evaluated in a temporal discrimination task. The observer was required to discriminate between two sequences of tone bursts. In one sequence the time interval between each tone burst was constant; in the other sequence the time interval was a random variable. A set of fixed and random pattern rules determined the frequency of each tone in the sequence. Discrimination performance was studied as a function of the magnitude of the time interval jitter and the serial pattern of tone frequency. Performance in the fixed pattern conditions was well described by a multiple-channel model in which timing information is available between tones within the same frequency region. The influence of higher order attentional factors was randomly determined. The frequency-selective mechanism appears to be sensitive to uncertainty about the frequency pattern of the input. Repeating the random pattern within each trial effectively eliminated this uncertainty. This result is consistent with experiments on the discrimination of word-length auditory patterns and temporal cues in speech.

Signal detection in computer-synthesized noise.

Human observers detected sinusoidal and pulse-train signals in noise derived from two computer-synthesized sources and from a Gaussian noise source. The synthesized noise stimuli were generated from sequences of pulses whose amplitudes were drawn from two divergent types of probability distributions: a centrally peaked distribution and a bimodal distribution. No differences in the detectability of signals in these noise stimuli were evident at pulse rates of 1000, 2000, 4000, or 10 000 Hz. subjects could not discriminate between the two types of computer-generated maskers at any pulse rate. The data support a spectrum-analyzer model of detection in which multiband filtering of the input smooths the masker energy in each spectral region to approximate the Gaussian case.