ABSOLUTE IDENTIFICATION OF TEMPORAL INTERVALS: PRELIMINARY DATA Yves Lacouture1, Simon Grondin1, and Shuji Mori2 1 Université Laval, Québec, Canada, 2Tokyo Metropolitan University, Japan
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Abstract In two experiments, participants performed absolute identification of time tasks involving intervals marked by auditory signals. In both experiments, the typical bow effects and other behavioral phenomena generally reported for the absolute identification of sensory signals were also observed for time intervals. These results are argued to be consistent with the idea that sensory processes do not solely explain behavioral phenomena in absolute identification, but also depend on decision and response mechanisms.
A typical absolute identification task involved a set of N stimuli that varied along a perceptual continuum. For each trial, one of the N stimuli was presented and the participant’s task was to identify it with a unique pre-specified label. It is generally recognized that in such experiments, which involve unidimensional perceptual stimuli, humans can correctly identify no more than 7 (± 2) stimuli (see Miller, 1956, for an early review, and Shiffrin & Nosofsky, 1994, for a contemporary discussion of that classic paper). However, it has been recently argued by Cowan (2001) that this processing capacity is limited to 4 (± 1) rather than 7 stimuli. This limited processing capacity is intriguing for several reasons. First, it is very general and holds for the identification of unidimensional visual, auditory, gustatory, and tactile stimuli. Second, extensive practice only leads to slight improvement during the initial learning stage, with performance asymptoting quickly thereafter. Third, performance limitation is observed even in conditions involving pairwise perfectly discriminable stimuli. Different fundamental phenomena in absolute identification, like the set-size effect and the bow effect, have been observed in numerous experiments (for recent reviews see Shiffrin & Nosofsky, 1994, and Lacouture, 1997). The set-size effect refers to the fact that as the number of stimuli increases performance quickly reaches an asymptotic level. With the so-called bow effect, responses are more accurate and faster at the ends of the stimulus continuum, with accuracy decreasing and response time increasing toward the center. Two Component Processes: Stimulus Representation and Response Selection. Psychophysical judgments are frequently assumed to involve two component processes, one associated with stimulus representation, the other with response selection. Most explanations for performance limitations in absolute identification are couched within the Thurstonian framework of sensory scaling (see Luce, 1994, for a recent appraisal) and, consequently, emphasize the processes and mechanisms associated with stimulus representation. Within the Thurstonian framework, each (unidimensional) stimulus is assumed to give rise (within and between trials) to a distribution of “perceptual effects” along a unidimensional continuum. The variability is often attributed to stimulus (or sensory) noise. Furthermore, it is assumed that the observer partitions the stimulus range into different response regions, using a set of decision criteria. The decision criteria are also assumed to be variable (there is criterion noise). Different aspects of performance limitations in absolute identification are then
postulated to be for the most part a result of the variability in the internal or psychophysical stimulus representations. Another class of absolute identification theories emphasizes the role of the response selection process. For instance, Lacouture and Marley’s (1991, 1995) mapping model proposes that some of the behavioral phenomena, including the bow effect, can be explained by the constraint involved when a unidimensional stimulus representation is mapped to (multidimensional) response categories. This constraint mapping process implies higher probability correct and shorter response times for stimuli located toward the ends of the stimulus continuum. Categorization of time intervals There are some theoretical and empirical reasons for believing that duration represents a different class of sensory stimulation; a type of stimulation that would be processed with specific perceptual mechanisms. From a theoretical standpoint, time can hardly be seen as a stimulus, and there is no direct evidence that there are “temporal” receptors similar to auditory or visual receptors (Grondin, 2001). From an empirical viewpoint, a number of researchers have reported data showing that the classic methods employed in psychophysics often do not yield the same pattern of results with duration as with other sensory stimulations (e.g., Allan & Kristofferson, 1974). These authors reported that, "It appears that the processing of duration discrimination differs in some fundamental way from the processing of other sensory information (amplitude, pitch, movement, position)." (p. 28). They based their conclusion on the respective effects of psychophysical methods on temporal and nontemporal performances. When two successive stimuli to be discriminated are presented, the time interval between the stimuli is known to influence performance. This effect does not apply to the discrimination of time intervals (Allan, Kristofferson, and Rice, 1974; Small and Campbell, 1962). It is also known that discrimination of simple sensory stimuli is better with a forced-choice procedure than with a single-stimulus procedure (Creelman and Macmillan, 1979). Again, this effect is not observed for discrimination of time intervals (Allan et al., 1974; Carbotte, 1973). Goal of the study As stated earlier, numerous studies have shown that the basic behavioral phenomena observed in absolute identification hold for various sensory signals. One can argue that this was due to the fact that the identification task involved representation spaces and decision processes independent of the sensory modality. Provided that a stimulus set is unidimensional and organized in increasing magnitude along a continuum, the basic behavioral phenomena should be observed. An interesting question is whether this is true for time intervals. Although not a sensory signal, time intervals of variable duration can be organized along an increasing unidimensional continuum. The goal of the present study was thus to verify whether the classic bow and set-size effects would also be observed in absolute identification of empty time intervals. Two experiments are reported. In the first, participants performed an absolute identification task involving a stimulus set made up of ten time intervals. In the second, participants performed an absolute identification task involving stimulus sets made up of 2, 4, 6, 8, and 10 time intervals.
Experiment 1: Bow effect Method Participants Eight volunteer undergraduate students received CDN $10 for their participation in two experimental sessions. All participants reported having normal or corrected to normal vision, and no one reported having a motor handicap. Apparatus The experiment was conducted in a dimly lit, sound-attenuated chamber. Each participant performed an absolute identification task involving ten empty time intervals delimited by two 1000 Hz auditory signals that lasted 20 ms and that were presented monaurally using a Sennheiser HD-545 headset. An MS-DOS-286 computer running Micro Experimental Laboratory software (MEL) was used for the stimulus presentation and response recording. Coulbourn modules controlled through an i/o computer card were used to generate the auditory signals. Instructions and feedback were presented on a VGA screen located approximately 120 cm away from the participant. Responses were collected using a custom-made keyboard with 11 buttons. One button, labelled "START", was located at the center of the ten other buttons, which were positioned in a semi-circle such that the distance between the START button and each of the other response buttons was equal (101 mm). The keyboard was placed such that participants were able to use their dominant hand. Each response button corresponded to one of the ten possible stimuli, and the button arrangement corresponded to the natural ordering of the stimuli from the shortest (leftmost) to the longest (rightmost). Response time–the time elapsed between the offset of the second marking auditory signal and key press–was recorded and timed in milliseconds using MEL timing routines. Procedure The ten time intervals lasted 400, 464, 538, 624, 724, 840, 975, 1130, 1311, and 1521 ms. Consequently, each adjacent pair of stimuli had a 16% difference. These intervals were given "correct" response labels of “1” to “10.” Each session involved a total of 300 trials (30 for each stimulus). The participants were instructed to respond as rapidly and accurately as possible. The participant initiated each trial by pressing the START button. One randomly selected stimulus was presented 100 ms later. The participant had to identify the stimulus by pressing the appropriate response button. One second after the participant's response was recorded, feedback was provided for 1 s in the form of a number presented on the computer screen that corresponded to the ordinal position of the stimulus. If the participant provided an incorrect response, the background of the computer screen turned red for 500 ms. A trial ended with the presentation of a blank screen. If the participant waited more than 30 seconds before pressing the START button to begin the next trial, a short sequence of three tones was generated to regain the participant's attention. Results Probability corrects (PC) and mean response times (MRT) were computed for each stimulus (1 to 10). Trials associated with extreme response time values (2% at each extreme of the percentile distribution for each condition) were removed. Only correct trials were used for response time analysis. The data were averaged across participants for each interval. Figure 1 summarizes the group results. The overall probability correct is 68%. For both PC and MRT, the results reproduced the typical bow effect usually observed for absolute identification when ten stimuli are used (Lacouture, 1997). As can be seen, PC drops from around 0.8 for Stimuli 1
and 10 to 0.4 for the stimuli located in the middle of the stimulus set. Similarly, MRT rose from around 600 ms and 700 ms at the extremes of the stimulus set to over 1 s in the middle of the stimulus continuum. Note that for the MRT, the bow curve is slightly asymmetric, with better performance for Stimulus 10 than Stimulus 1. 1200
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Figure 1. Results of Experiment 1. Probability correct (left panel) and mean response time (right panel) plotted as a function of stimulus position (labelled 1 to 10).
Experiment 2: Set-size effect Method Participants Eight volunteer undergraduate students received CDN $25 for their participation in ten experimental sessions. The participants were not the same as in Experiment 1. All participants reported having normal or corrected to normal vision, and no one reported having a motor handicap. Apparatus The material was the same as in Experiment 1. Procedure Five stimulus sets–with 2, 4, 6, 8, or 10 elements–were used in ten experimental sessions (two for each stimulus set). For set size 10, the duration of the ten time intervals in ms was the same as in Experiment 1, with the same response labels. The other stimulus sets were subsets of the 10 stimuli set. For set size 8, stimuli “2” to “9” were used, for set size 6, stimuli “3” to “8” were used, and so on. Each session involved a total of 400 trials (40 for each stimulus). As in Experiment 1, the participants were instructed to respond as fast and accurately as possible. The order of presentation of the stimulus sets was randomly selected.
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Figure 2. Results for Experiment 2. Overall probability correct (left panel) and mean response time (right panel) plotted as a function of set size.
Results The probability of responding correctly (PC) and the mean response time (MRT) were computed for each stimulus within each stimulus set. As in Experiment 1, trials associated with extreme response time values (2% at each end of the distribution) were removed and only correct trials were used for response time analysis. Overall PC and MRT plotted according to set size are presented in Figure 2. As can be seen, PC decreases with increasing set size while MRT increases with increasing set size. Results for stimulus sets plotted according to stimulus position are presented in Figure 3 where the left panel presents PC and the right panel presents MRT. Each line on the graph corresponds to one of the stimulus set with set sizes 2, 4, 6, 8, and 10. The figure shows that both PC and MRT exhibit the expected bow effect and that better performances are observed toward the end of the continuum as set size increases.
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Figure 3. Results for Experiment 2. Probability of responding correctly (left panel) and mean response time (right panel) plotted as a function of stimulus position (labelled 1 to 10).
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Conclusion The preliminary results presented in this paper show that the performance limitation and the bow effect observed for the absolute identification of sensory signals are also observed for the absolute identification of empty time intervals. Although time intervals are different from sensory signals, the results suggest that the internal representation and decision process involved in the absolute identification of time interval are the same as the representation and decision process for the absolute identification of sensory signals. This result is congruent with the proposition that the behavioral phenomena in absolute identification depend on representation and decisions processes. References Allan, L. G., & Kristofferson, A. B. (1974). Psychophysical theories of duration discrimination. Perception & Psychophysics, 16, 26-34. Allan, L. G., & Kristofferson, A. B., & Rice, M. E. (1974). Some aspects of perceptual coding of duration in visual duration discrimination. Perception & Psychophysics, 15, 83-88. Carbotte, R. M. (1973). Retention of time in forced choice duration discrimination. Perception & Psychophysics, 14, 440-444. Cowan, N. (2001). The magical number 4 in short term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, Creelman, C. D., & Macmillan, N. A. (1979). Auditory phase and frequency discrimination: a comparison of nine procedures. Journal of Experimental Psychology: Human Perception and Performance, 5, 146-156. Grondin, S. (2001). From physical time to the first and second moments of psychological time. Psychological Bulletin, 127, 22-44. Lacouture, Y. (1997). Bow, range, and sequential effects in absolute identification: A response-time analysis. Psychological Research, 60, 121-123. Lacouture, Y., & Marley, A. A. J. (1991). A connectionist model of choice and reaction time in absolute identification. Connection Science, 3, 401-433. Lacouture, Y., & Marley, A. A. J. (1995). A mapping model of the bow effect in absolute identification. Journal of Mathematical Psychology, 39, 383-395. Luce, R. D. (1994). Thurstone and sensory scaling: Then and now. Psychological Review, 101, 271-277. Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63, 81-97. Shiffrin, R. H. , & Nosofsky, R. M. (1994). Seven plus or minus two: A commentary on capacity limitations. Psychological Review, 101, 357-361. Small, A. M., & Campbell, R. A., (1962). Temporal differential sensitivity for auditory stimuli. American Journal of Psychology, 75, 401-410.
Acknowledgments This research was supported by grants from the Natural Science and Engineering Research Council of Canada (NSERC) to YL and to SG, a grant from Fonds FCAR (Québec) to YL, and a grant from the Japanese Ministry of Education, Sports, and Culture to SM.
