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Detection and recognition of increments and decrements in auditory intensity* NEIL A. MACMILLAN Brooklyn College of the City University of New York Brooklyn, New York 11210 Os' performance in the detection of increments and decrements in the intensity of a pure tone was compared with their performance in an increment·decrement recognition experiment. Recognition performance improved, relative to detection performance, as signal duration increased. This is surprising from the point of view of all stimulus models within signal detection theory. These data and others are described in terms of a change detection mechanism. The first section of this paper is a se Ie c tive summary of signal detection theory (SDT), with stress on stimulus models for detection and recognition experiments. Among the assumptions shared by such models are (1) that the 0 integrates information from the stimulus waveform over time, and (2) that a set of stimuli differing only in intensity gives rise to internal effects differing on only one dimension. Auditory data are later presented which violate both these assumptions, and a model incorporating both integrative and nonintegrative modes of detection is proposed to deal with these data. The fundamental tenet of SDT, borrowed from Thurstone (1927), is that the repeated presentation of the same stimulus gives rise to a distribution of sensory effect. If there are two possible stimuli, the 0 is presumed to order the possible sensory events according to the likelihood ratio (the relative likelihood of their having arisen from one of the stimuli), and to establish a cut-point decision rule on the likelihood ratio axis. If some assumptions are made about the form of the underlying distributions, then the O's sensitivity can be described by parameters which are unaffected by bias. The assumption usually made, also originally by Thurstone (1927), is that the distributions arising from the two possible stimuli are normal. If ROC curves are collected by the • Based on part of a dissertation submitted to the University of Pennsylvania in partial fulfillment of the requirements for

the PhD degree. The author wishes to thank Dorothea J. Hurvich, R. Duncan Luce, Elizabeth F. Shipley, and James L. Zacks for their help with many aspects of this research, and also Jack CatliD, C. Douglas Creelman, Irwin PoUack, and' Don L. Scarborough for their helpful comments on previous versions of this manuscript. Partial support for the investigation was provided by the Society of Sigma Xi.

manipulation of biases, it is possible to estimate two parameters (Green & Swets, 1966, p. 96): am, the difference between the means of the two distributions, divided by the standard deviation of one of them; and s, the ratio between the standard deviations of the two distributions. If it is assumed that s = I, then Am is usually called d' and can be estimated without manipulating biases. INTEGRATIVE MODELS FOR DETECTION Since Am and s (or d') reflect only se nsory factors, changes in the experimental situation which result in changes in these parameters must, according to SDT, be affecting the sensory experience of the 0 rather than simply his response rules. Thus we may ask: What aspects of pairs of stimuli affect an O's d'? This is a statement, within SDT, of the "recognition problem." If one of the two possible stimuli is the null stimulus 0, the problem is called "detection" (Luce, 1963). Many solutions to the detection problem in audition have been proposed. Some are "ideal detectors" (Green & Swets, 1966, Chap. 6), in the sense that all the information available in the stimulus is used to compute a statistic monotonic with the likelihood ratio. The 0 is assumed to compute this statistic from a finite number of observations during the signal interval. Energy detection is the most generally applicable of the rules used by ideal Os (for the case in which the signal is a sample of broadband noise), and the rule has been extended to apply to conditions for which it is not ideal (Green & Swets, 1966, Chap. 8; McGill, 1967). The reasoning behind this application of energy detection is that the human 0 may only estimate the energy of the signal, even when other relevant information is in principle available to him.

Perception &; Psychophysics, 1971, Vol. 10 (4A)

Experimental investigation within the framework of SDT suggests that human detectors are not ideal, but may be energy detectors in some stimulus conditions (Green & Swets, 1966, Chap. 8). All detectors imagined so far by SDT, however, have In common that their performance improves as stimulus duration increases. 1 This property, which is a result of the finite sampling hypothesis mentioned above, leads us to ch aracterize SDT detectors as "integrative." This is not to suggest that the only accomplishment of SDT has been to describe detectors as integrative, but rather to stress that duration is virtually the only important stimulus property, aside from intensity. on which all proposed detectors depend. THE THREE-STIMULUS PROBLEM If S ={Sa,Sb'Sc. is a set of stimuli, there are t h r e e possible co mplete-identification experiments (Bush, Galanter, & Luce, 1963) of the yes-no design which can be performed using two-element subsets of S. According to SOT, the effect of each stimulus, sx' is characterized by a mean, Il (Sx), and a variance, (J 2 (sx)' If the variances are all equal, then each of the three experiments is characterized by a d' Xy(x,y = a.b,c; x y). We wish to know, for a given set S, what relationship holds between the various d' xy' It has usually been assumed that, at least when the three stimuli differ only in intensity, the distributions generated by them may be considered to lie upon a single decision axis (see, for example, Tanner, 1956). This assumption, referred to henceforth as the linearity condition, has been supported in both auditory and visual amplitude discrimination studies (e.g., Creelman. 1963; Nachmias & Kocher, 1970). From this assumption, if /J(sa) . Decrement detect ion Q-----SV

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DISCUSSION o c. The most obvious failure of SDT Fig. 6. Results of forced-choice o models in accounting for the preceding mixed-duration increment detection a. 1.0 results is that the linearity condition is experiment (Experiment 5). frequently not met (see Experiments .9 1,2, and 3). More important, however, more quickly than the In, but both is the fact that this condition is more the CD and the ID are used in .8 nearly satisfied at long durations than situations (such as detection) for .7 at short ones. If recognition which they are partially redundant, performance . bore some consistent then the CD is probably wasteful of .6 KR '--,---.. relation to detection performance information in some way. other than that specified by the A model incorporating two 100 225 15 600 50 linearity condition, then this condition mechanisms, an ID and a CD, can could be simply replaced by a more account for the data of Duration in msec. general one without affecting the Experiments 1-4. To understand why other assumptions of SDT models. In recognition improves more rapidly Fig. 5. Results of forced-choice fact, Tanner (1956) has proposed a with duration than detection, assume uncertain detection experiment model in which the internal effects that the 0 does not use the CD for (Experiment 4). due to three stimuli are located on a recognition, as this mechanism is plane rather than on a line. The degree insensitive to the direction of change. Results of failure of the linearity condition is Since detection involves both Data are given in Fig. 5. The reflected by an added free parameter, e, integration and change detection deterioration due to uncertainty is the angle formed by the intersection (complete nonintegration), detection greatest at 600 msec; no convincing of lines connecting the means of two performance must improve more duration effect is evident between 15 pairs of distributions. Such a model slowly with duration than and 225 msec. No duration effect of does not provide a satisfying re cognition, which involves only any kind is predicted by SDT. Two understanding of the present results, integration. The CD is very useful at aspects of these data are disconcerting however, since different values of () are short durations, so detection for SDT: there seems to be no deficit required for different signal durations. performance is relatively better there. in performance due to uncertainty for Reporting that () increases with signal At long durations, the CD is hardly Os RZ and KR between 15 and duration is no improvement on needed, so detection falls well below 225 msec; and, for all Os, the observed reporting that the disparity between recognition. If detection involves change deficit is a function of duration, recognition performance and detection reaching a maximum at 600 msec. performance increases with signal detection, then k, the exponent of T duration. in the time-intensity tradeoff relation, There is ample evidence, here and will be smaller than predicted by EXPERIMENT 5: FC MIXED-DURATION elsewhere, that 'detection depends on completely integrative theories such as INCREMENT DETECTION an integrative detector (ID). However, SDT. The data presented in Fig. 4 and it may also depend on a nonintegrative Table 1 are consistent with this Aims and Procedures Th e results of the preceding mechanism. Suppose that an ID prediction. experiments are, to varying degrees, combines with a change detector (CD) In uncertain increment-decrement inconsistent with SDT. Experiment 5 with the following properties: detection (Experiment 4), the CD was performed to shed light on an (1) change detection of a signal is should be i!lst as useful as in the alternative model, to be proposed in independent of the duration of the corresponding certain detection the discussion section. signal. That is, the CD detects signal experiments, since it is insensitive to Signals were increments of four onsets (and possibly offsets). (2) The the direction of change. Thus, a model different durations (but the same CD is insensitive to the direction of incorporating change detection amplitude). A FC paradigm was used, change. If I is an increment in the predicts little deterioration in the signal duration on each trial being background and D a decrement, then performance at short durations (where selected randomly. The four durations the sensitivity of the CD is monotonic the CD's contribution is great) and (15,50, 100, and 225 msec) were increasing with (the absolute value of) maximum deterioration at longer equiprobable. I and also monotonic increasing with durations, where the ID is more A session consisted of 150 trials of the absolute value of D. This has important. Thus, the data (which show each duration in a block, preceded by intuitive appeal. If the CD operates maximum deficit at the longest

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duration, hut no systematic trend in the four shorter durations) are better understood in terms of a model of change detection than in a pure SDT context. Since, according to the model, the deficit in performance due to uncertainty (in Experiment 4) and the difference between recognition and detection (Experiment 3) derive from the same source, it is comforting that there is a positive relation between these two measures (p < .01 by Spearman correlation). 3 Previous experiments verifying the linearity condition (Creelman, 1963; Nachmias & Kocher, 1970) have not used decrements as signals. If the sensitivities of the IV and the CD as a function of signal intensity are similar for signals which add energy to the background, then the linearity condition will obtain in amplitude discrimination even with Os invoking both mechanisms. Thus, there is no contradiction between earlier findings that the linearity condition holds at short durations and the present finding that it does not. If the notion of change detection is accepted as a tentative explanation of these results, several questions may be asked. First, how do the ID and the CD combine? Suppose that, on a given trial, either the ID is used or the CD, but not both, and the O's response depends entirely on the detector he uses. Then the results of Experiments I, 2, and 3 can only be accounted for by supposing that the probability of using the CD is a function of duration. In that case, if durations are randomized, the (constant) probability of change detection that is adopted must be less than optimal for at least some durations, and performance will be poorer than if blocks of signals of the same duration were presented. The results of Experiment 5 indicate that this is not so, and accordingly we reject the possibility that the CD is used only when the ID is not. Apparently both the CO and the 10 may be used in processing a given waveform. Furthermore, any model for combining the outputs of the ID and CD in which the nature of the combination is susceptible to strategies of the 0 must be rejected. In other situations, the 0 may be able to manipulate the relative weight given to the two mechanisms (he can apparently ignore the CD in

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recognition experiments, for example), but it is clear that he does not do so in the detection conditions. Although these data put severe restrictions on the construction of a model for the combination of the ID and CD, many possibilities remain. For example, the 0 in a yes-no experiment coul d respond 'yes' if both mechanisms reported a detection or if either did. Or the outputs of the two detectors could be added to yield a decision variable. If assumptions are made about the sensitivity of the CD, then models of its combination with the ID should be testable. A second question is: How does the CD work? One possibility is that change detection is Fourier analysis of the waveform followed by a high-pass filter. This is reasonable, since signal onsets are high-frequency events. An alternative model would detect changes by double differentiation of the waveform. None of the results reported bear on this issue. CONCLUSION The results of several experiments have been presented to argue that integrative SDT models are inappropriate for the understanding of detection and recognition experiments, and that a combination of change and integrative detection provides a useful alternative. It is important to distinguish, however, two roles that are frequently played by SOT. First, it is used to take account of bias effects in an experiment. Although, according to the current analysis, this is not completely safe, SOT is still useful for this purpose. Also, however, SOT provides a framework for the investigation of perception which has led to the conclusion that all detection is integrative. The major significance of the current investigation is its demonstration that this conclusion is incorrect. REFERENCES BARLOW. H. B. Temporal and spatial summation in human vision at different background intensities. Journal of Physiology. 1958,141,337-350. BUSH, R. R. Estimation and evaluation. In R. D. Luce, R. R. Bush, and E. Galanter (Eds.), Handbook of mathematical psychology. Vol. 1. New York: Wiley, 1963. BUSH. R. R., GALANTER, E., &: LUCE, R. D. Characterization and classification of choice experiments. In R. D. Luee, R. R.

Bush, and E. Galanter (Eds.), Handbook of mathematical psychology. Vol 1. New York: Wiley, 1963. CREELMAN, C. D. Detection, discrimination, and the loudness of short tones. Journal of the Acoustical Society of America, 1963, 35, 1201-1205. GARNER. W. &: MILLER, G. A. Differential sensitivity to intensity as a function of the duration of the comparison tone. Journal of Experimental Psychology. 1944, 34, 450-463. GREEN, D. M. Some comments and a correction of "Psychoacoustics and detection theory." Journal of the Acoustical Society of America, 1961, 33. 96&. GREEN, D. M., &: SWETS. J. A. Signal detection theory and psychophysics. New York: Wiley, 1966. LUCE, R. D. Detection and recognition. In R. D. Luce, R. R. Bush, and E. Galanter (Eds.), Handbook of mathematical tnscnotoe». Vol 1. New York: Wiley. 1963. MACMILLAN, N. A. Change detection-A model and some experiments on the perception of changes in auditory intensity. Unpublished doctoral dissertation, University of Pennsylvania, 1970. McGILL, W. J. Neural counting mechanisms and energy detection in audition. Journal of Mathematical Psychology, 1967, 4, 351-376. McGILL. W. J.. & GOLDBERG, J. P. Pure-tone intensity discrimination and energy detection. Journal of the Acoustical Society of America. 1968. 44, 576-581. NACHMIAS. J., &: KOCHER. E. Visual detection and discrimination of Iuminance increments. Journal of the Optical Society of America, 1970, 60, 382-389. TANNER, W. P. Theory of recognition. Journal of the Acoustical Society of America. 1956, 28, 882-888. THURSTONE. L. L. A law of comparative judgment. Psychological Review, 1927, 34,273-286. TREISMAN, M. Noise and Weber's law: The discrimination of brightness and other dimensions. Psychological Review, 1964, 71, 314-330. NOTES 1. This is also true of detectors proposed for vision. although the rationales underlying them are somewhat different. See, for example, Barlow (1958) or Treisman (1964). 2. When signals are changes in the intensity of a pure tone and /::.v/v is small. AliI,; 2/::'vlv (Green, 1961). Thus, the exponent estimated by plotting Aviv is identical to that estimated by plotting AliI or, since I is constant. Al itself. 3. The measures used were (1) the average proportion correct in increment and decrement detection, minus the proportion correct in uncertain detection; and (2) the proportion correct in recognition minus the average proportion correct in increment and decrement detection. (Accepted for publication March 4, J 971.)

Perception & Psychophysics, 1971, Vol. 10 (4A)