Duration-discrimination data from an experiment using empty auditory intervals in a two-alternative forced-choice paradigm are presented. The observed functional relationship between standard deviation of the psychometric density function and stimulus duration is shown to be fit significantly better by a Weber's law model of duration discrimination than by Creelman's counter model. Both models fail to predict the rapid rise in the Weber fraction observed for durations longer than about 2 sec. However, the Weber's law model, based on a generalization of Weber's law, accurately predicts the initial drop in the Weber fraction for very short durations and the observed constancy of the Weber fraction for durations up to 2 sec.Weber's law has endured as a useful empirical description of the relationship between discriminability and stimulus magnitude for a number of intensive sensory dimensions (Holway & Pratt, 1936; Luce & Galanter , 1963;Miller. 1947). However. in reviewing a number of studies of duration discrimination, both Allan and Kristofferson (1974) and Woodrow (1951) conclude that Weber's law does not hold for duration. The studies they cite cover a range of durations from .63 msec to 30 sec. While the evidence they present argues strongly that their conclusion is correct for that entire range of durations, the possibility remains that Weber's law', or perhaps a generalized form, holds for some more limited range.Several recent studies of human duration discrimination (Abel. 1972a, b; Kinchla, 1972) have provided some support for a counter model of human timing tirst proposed by Creelman (1962). Whereas Creelman tested durations from .25 to .80 sec and found that the counter model predicted discriminability well over the entire range, Abel (l972a) concluded that the model did reasonably well only for durations less than about .1 sec. failing for longer durations. On the other hand. Kinchla (1972) found support for the counter model over a range of 1 to 8 sec.In this paper. the counter model and aWeber's law model. based on a generalization of Weber's law, are outlined and several predicted functions derived. The two models are then compared in terms of their ability to account for the data from a duration discrimination experiment also reported here.This research was supported by Public Health Service Grant MH24143 to the author. I wish to express my gratitude to Marilyn Adams and Seth Roberts for their helpful comments and suggestions, and especially to Russell Church for his critical discussions of this research with me on numerous occasions. I also wish to thank Tom Wing for his help in designing the experiment and his participation as a subject. Requests for reprints should be sent to David J. Getty, Psychology

An automated detector designed to warn a system operator of a dangerous condition often has a low positive predictive value (PPV); that is, a small proportion of its warnings truly indicate the condition to be avoided. This is the case even for very sensitive detectors operating at very strict thresholds for issuing a warning because the prior probability of a dangerous condition is usually very low. As a consequence, operators often respond to a warning slowly or not at all. Reported here is a preliminary laboratory experiment designed in the context of signal detection theory that was conducted to examine the effects of variation in PPV on the latency of participants' response to a warning. Bonuses and penalties placed premiums on accurate performance in a background tracking task and on rapid response to the warnings. Observed latencies were short for high values of PPV, bimodal for middle-tolow values, and predominantly long for low values. The participants' response strategies for different PPVs were essentially optimal for the cost-benefit structure of the experiment. Some implications for system design are discussed.

http://radiology.rsna.org/lookup/suppl/doi:10.1148/radiol.11091276/-/DC1.

A psychophysical procedure was used to determine the difference limen for the duration of a signal that ranged from .5 to 8.0 sec. The accuracy of three rats in keeping track of the duration was assumed to be limited by three factors: (a) inattention to the signal on some trials, (b) variability in starting to time the duration when the signal begins (and/or in stopping to time the duration when the signal ends), and (c) factors related to signal duration itself. A generalized Weber model provided a better approximation to the growth in the difference limen as a function of signal than a generalized Counter model.

A general protocol for rigorous evaluation of diagnostic systems in medicine was applied successfully in a comparative study of two radiologic techniques. Accuracies of computed tomography and radionuclide scanning in detecting, localizing, and diagnosing brain lesions were assessed with a sample of patients in whom tumor had been suspected. The principal means of analysis was the "relative operating characteristic," which is unique in providing a measure of accuracy that is largely independent of decision biases. Computed tomography was found to be substantially more accurate than radionuclide scanning.

A subject reproducing a long duration, t, may time out either a single interval of duration t or a succession of n intervals, each of duration tIn. It is shown that a class of timing models obeying Weber's law predicts the variance of reproductions of t to be a decreasing function of the number of subdivisions, n. In contrast, a second class of proportional variance models, which includes Creelman's pulse counter model (1962), predicts no change in the variance as a function of n. Data are presented from a duration reproduction experiment in which subjects counted silently at a specified rate up to a given number and then responded. Several statistics involving the variance of the reproduced durations are shown to be predicted significantly better by the Weber's law class of models than by the proportional variance class of models.

Techniques that may enhance diagnostic accuracy in clinical settings were tested in the context of mammography. Statistical information about the relevant features among those visible in a mammogram and about their relative importances in the diagnosis of breast cancer was the basis of two decision aids for radiologists: a checklist that guides the radiologist in assigning a scale value to each significant feature of the images of a particular case, and a computer program that merges those scale values optimally to estimate a probability of malignancy. A test set of approximately 150 proven cases (including normals and benign and malignant lesions) was interpreted by six radiologists, first in their usual manner and later with the decision aids. The enhancing effect of these feature-analytic techniques was analyzed across subsets of cases that were restricted progressively to more and more difficult cases, where difficulty was defined in terms of the radiologists' judgements in the standard reading condition. Accuracy in both standard and enhanced conditions decreased regularly and substantially as case difficulty increased, but differentially, such that the enhancement effect grew regularly and substantially. For the most difficult case sets, the observed increases in accuracy translated into an increase of about 0.15 in sensitivity (true-positive proportion) for a selected specificity (true-negative proportion) of 0.85 or a similar increase in specificity for a selected sensitivity of 0.85. That measured accuracy can depend on case-set difficulty to different degrees for two diagnostic approaches has general implications for evaluation in clinical medicine. Comparative, as well as absolute, assessments of diagnostic performances--for example, of alternative imaging techniques--may be distorted by inadequate treatments of this experimental variable. Subset analysis, as defined and illustrated here, can be useful in alleviating the problem.

Three observers viewed visual representations of eight complex sounds in both a pairwise similarity-judgment task and an identification task. A multidimensional scaling procedure applied to the similarity judgments yielded a three-dimensional perceptual space and the relative positions of the stimuli in that space. A probabilistic decision model based on weighted interstimulus distances served to predict well the confusion matrices of the identification task. Three conditions of the identification task, calling for identification of different subsets of the eight stimuli, led the observers to vary the weights they placed on the dimensions; they apparently adjusted the weights to maximize the percent correct identification. An additional group of 14 subjects, participating only in the similarity-judgment task, manifested the same three dimensions as the observers (corresponding to the locus of low-frequency energy, the locus of midfrequency energy, and visual contrast), and also a fourth dimension (corresponding to the periodicity, or waxing and waning, of the sound). Although not evident in the scaling analysis for the three observers, our utilization of the additional dimension increased significantly the variance accounted for in their identification responses. The overall accuracy of the predictions from a perceptual space to identification responses supplies a substantial validation of the use of multidimensional scaling procedures to reveal perceptual structure in demonstrating the ability of that structure to account for behavior in an independent task. The empirical success of this approach, furthermore, suggests a relatively simple and practical means of predicting, and possibly enhancing, identification performance for a given set of visual or auditory stimuli.A reasonably complete account of the process by which humans are able to identify complex auditory or visual stimuli must address two issues: (I) the nature of the psychological representation of complex stimuli, and (2) the nature of the decision processes that act upon the internal representations to yield an identification response. While there has been substantial research directed at the representation and decision processes separately, there has been much less effort directed towards understanding the integration of these processes in the identification of complex stimuli. Our major concern in this paper is with the relationship between perceptual representation and identification performance. The question is, given specific assumptions about the structure of the perceptual space, how well can we account for the pattern of responses observed in an identification task?Our approach to the problem involves two parts: (I) the derivation of a multidimensional perceptual space for a set of complex stimuli from the application of a multidimensional scaling (MDS) procedure to judgments of stimulus similarity, and (2) the use This research was supported by a contract with the Engineering Psychology Programs, Office of Naval Research. We thank Barbara...