Perception, 1977, volume 6, pages 703-709
The perception of brief temporal intervals: power functions for auditory and visual stimulus intervals
Douglas J Bobko, Jack G Thompson, Harvey R Schiffman Department of Psychology, Rutgers, The State University, New Brunswick, New Jersey 08903, USA Received 25 January 1977
Abstract. Two experiments were performed to examine the role of method of estimation and the employment of a standard stimulus on the judged duration of auditory and visual stimuli presented for brief temporal intervals (0-25 to 5-0 s). The results indicate that the relationship between judged and physical duration is nearly direct and linear. Psychophysical methodology and stimulus modality exerted little influence on the obtained power functions. 1 Introduction Stevens and Galanter (1957) proposed that the relationship between the judged and the physical duration of a stimulus presentation is best described by a power function, i.e. duration belongs to the class of prothetic continua. However, empirical evidence concerning the value of the power function exponent is sparse and equivocal. Stevens (1960) and Stevens and Greenbaum (1966) reported that the judged duration of white noise within the range of 0-30-50-0 s is "almost a linear but slightly accelerating function of physical duration" (exponent of about 1-1). That is, judged duration increases at a slightly faster rate than physical increments. Eisler (1975), on the other hand, found the converse relationship: Judged duration is a decelerating function of physical duration, with an exponent of about 0 • 84 for auditory intervals ranging from 1-3-20-0 s. Accordingly, the present study was performed to assess the nature of the power function relating judged and physical duration by presenting a pure tone of fixed intensity for brief temporal intervals. Additionally, four different sets of instructions (verbal estimation and magnitude estimation, each with and without a standard stimulus) were employed to investigate the role of psychophysical methodology and the role of a standard stimulus on duration judgments. Although Stevens (1971) has argued that the use of a standard stimulus is unnecessary for many sensory-perceptual continua, there is a lack of empirical data on the effects of such manipulations in duration judgments. Theoretically, differences in the choice of a standard stimulus should effect changes in the intercept of the power function but not in the slope (Stevens 1971). Of subsidiary interest were possible differences in the psychophysical duration functions which result either from a well-practiced and familiar response language, e.g. direct verbal estimation in seconds, or a standard magnitude estimation procedure. 2 Experiment 1 2.1 Method 2.1.1 Subjects. Forty volunteers from an introductory course in psychology served as subjects. 2.1.2 Stimuli. The stimuli were twenty time intervals, ranging from 0-25 to 5-0 s in equal steps of 0 • 25 s. The stimulus intervals were defined by the onset and termination of a pure 1500 Hz tone. The intensity of the tone was measured at 35 dB (the reference level was 0-0002 /zbar).
704
D J Bobko, J G Thompson, H R Schiffman
2.1.3 Apparatus. The main testing apparatus consisted of a Sine Wave Generator (Dynascan, model E 31 OB), headphones, and a silent-running timer (Hunter, model 11 IB). The apparatus was concealed from the subjects. 2.1.4 Design and procedure. Four different psychophysical tasks were employed: (i) verbal estimation, (ii) verbal estimation with a standard stimulus, (iii) direct magnitude estimation, and (iv) magnitude estimation with a standard stimulus. In the two verbal-estimation conditions the subjects' task was to estimate the duration of each interval in seconds and fractions of a second, while in the magnitudeestimation tasks subjects were instructed to assign a numerical value to each interval to indicate its length. In both conditions with a standard stimulus, the first interval presented during testing was fixed at 2-5 s and served as the standard; in the verbalestimation-with-standard-stimulus condition the subjects were informed of the actual duration of the standard interval in seconds, while in the magnitude-estimation-withstandard-stimulus condition the subjects were instructed to assign the interval a value of 100. A between-groups design was employed. Ten subjects were randomly assigned to each of the four experimental conditions (instructions). Except for the instructions, the procedure was identical for all subjects. The subjects were seated in front of the apparatus, and their wristwatches were removed. Subjects assigned to the verbal-estimation conditions were read the following instructions: "This is an experiment on time perception. A tone will be presented for different intervals of time. I want you to estimate how long you think the tone is on for during each interval to the nearest second and fraction of a second. (i) Try to estimate the first interval as accurately as you can in seconds and fractions of a second. Thereafter try to keep your judgments proportional. For example, if you think that the first interval is 2 • 5 s long, any interval that you think is twice as long should be called 5 s, and any interval you think is half as long should be called 1 • 25 s. (ii) I am going to present the tone for 2-5 s for the first interval. Thereafter try to keep your judgments proportional. For example, any interval that you think is twice as long should be called 5 s, and any interval you think is half as long should be called 1-25 s. Please do not count or tap during the experiment. Do you have any questions?" Subjects assigned to the magnitude-estimation conditions were read the following instructions: "This is an experiment on time perception. A tone will be presented for different intervals of time. I want you to estimate how long you think the tone is on for during each interval in relation to the first interval. (iii) Choose any convenient and reasonable number to stand for the first time interval. Thereafter try to keep your judgments proportional. For example, if you think that any interval is twice as long as the first interval you should assign it a number twice as large. Any interval that you think is half as long as the first interval should be assigned a number half the value of the first interval. (iv) I am going to present the first tone for an interval length which you should call 100. Thereafter try to keep your judgments proportional. For example, any interval that you think is twice as long as the first interval should be called 200, and any interval you think is half as long should be called 50. Please do not count or tap during the experiment. Do you have any questions?"
The perception of brief temporal intervals
705
In the standard-stimulus conditions the standard tone of 2-5 s was presented first; then the tone was presented for the twenty time intervals. All intervals were presented to each subject in random order and different randomized orders were employed for each subject. The interstimulus interval was approximately 20 s, during which the subjects estimated the duration of the stimulus presentation. Room illumination was measured at 79 cd m~2. 2.2 Results and discussion For each experimental condition, the data were averaged across subjects by computing the geometric mean of the estimates for each presentation interval. Straight lines were fitted by regression analysis to the logarithms of duration estimates as a function of the logarithm of physical duration as shown in figure 1; the slopes, ^-intercepts, correlation coefficients, and F-values from the regression analyses are shown in table 1. The significant F values (each at p < 0-01) and corresponding high correlation coefficients suggest that the relationship between the logarithm of judged duration and the logarithm of physical duration is linear and thus conforms to a power function; also, since the exponents of the power functions are close to 1-0, the function relating judged and physical duration may simply be described as a nearly direct and linear one. In all four experimental conditions, judged duration is a slightly decelerating function of physical duration. In order to test whether the instructions significantly affected the subjects' judgments, a regression analysis was 2-2
1-8 1-4 1-0 0-60 0-20 -0-20
magnitude estimation with modulus magnitude estimation verbal estimation verbal estimation with modulus
-0-60
JL_
_L_
J
-0-20 0 0-20 0-60 Physical duration (lg s) Figure 1. Logarithmic plots of duration estimates by physical duration for four experimental tasks. Duration intervals were defined by a 1500 Hz tone. -0-60
Table 1. Power-function slopes, intercepts, correlation coefficients, and F-values by method of estimation for auditory and visual stimuli. Method
Slope
Correlation coefficient F(l,18)
Intercept
auditory visual auditory visual auditory Verbal estimation Verbal estimation with modulus Magnitude estimation Magnitude estimation with modulus Geometric mean
visual
auditory visual
0-95 0-90
0-98 1-03
0-24 0-0
0-07 -0-06
0-992 0-994
0-995 0-968
1142-63 1796-08 1379-52 267-10
0-92 0-99
0-91 1-09
0-85 1-59
0-45 1-46
0-982 0-995
0-983 0-986
484-81 1827-78
0-94
1-00
518-33 608-37
706
D J Bobko, J G Thompson, H R Schiffman
performed on each subject's estimates (lg units) and an analysis of variance was performed on the resulting exponents. (The slopes and correlation coefficients for each subject are shown in table 2.) The main effects due to instructions were not significant [F(3, 36) = 1-14]. This suggests that under the present conditions of testing, the methods of verbal and direct magnitude estimation and the presence or absence of a standard stimulus exert little influence on the subjects' judgments. It is of interest also to note that the slopes of the power functions varied considerably between subjects; the exponents ranged from 0-63 to 1-46. It should be emphasized that this is not an uncommon finding even when each subject makes several estimates per stimulus interval (see Eisler 1975, p 446). Indeed, Stevens (1960) notes that an exponent based on group data "... represents an average value and is not necessarily appropriate to a particular individual" (p 236). A number of researchers (Goldstone et al 1959; Behar and Bevan 1961; Goldfarb and Goldstone 1964; Stevens and Greenbaum 1966) have reported that the judged duration of a stimulus is affected by the stimulus modality employed. Specifically, a given interval defined by a visual stimulus is judged relatively shorter than an interval of equal duration defined by an auditory stimulus. Accordingly, experiment 2 was designed to investigate this phenomenon by substituting a visual target for the auditory stimulus employed in experiment 1. Since the stimulus intervals used were identical to those of the previous study, any difference in duration estimates between modalities, and for a given instructional set, should be manifest in a difference of the power function intercepts. That is to say, if an auditory-stimulus duration appears longer than a physically equal duration of a visual stimulus, then the numerical values assigned to the auditory stimuli should be larger than those assigned to equivalent visual stimuli. Table 2. Individual slopes and correlation coefficients for each method of duration estimation (auditory stimulus). Subject Verbal estimation
1 2 3 4 5 6 7 8 9 10
Verbal estimation with modulus
Magnitude estimation
Magnitude estimation with modulus
slope
r
slope
r
slope'
r
slope
r
1-11 0-99 0-97 0-83 0-97 0-91 0-86 0-84 0-63 0-87
0-95 0-99 0-98 0-89 0-91 0-97 0-94 0-92 0-77 0-94
0-75 1-46 0-80 0-88 0-97 0-93 0-87 1-02 0-73 0-98
0-96 0-96 0-96 0-97 0-96 0-96 0-98 0-84 0-95 0-97
1-07 1-08 0-92 0-76 1-01 1-01 1-32 1-06 0-79 1-05
0-93 0-98 0-97 0-94 0-98 0-98 0-95 0-96 0-96 0-92
0-97 0-93 0-66 0-65 0-85 0-96 0-92 0-82 1-22 0-82
0-97 0-96 0-94 0-93 0-98 0-96 0-97 0-96 0-97 0-97
3 Experiment 2 3.1 Method 3.1.1 Subjects. Forty volunteers from the same population as the subjects in experiment 1 served as subjects. 3.1.2 Stimuli. The stimuli were the twenty time intervals employed in experiment 1. A small black 'X' subtending a visual angle of 1°14' served as the stimulus target. The target was constructed from 1 • 5 mm wide black graph tape mounted on a card of white poster board. During the testing, the midpoint of the target was congruent with the center of the presentation field.
The perception of brief temporal intervals
707
3.1.3 Apparatus. The main testing apparatus was a two-channel tachistoscope (Gergrands, model TIC). The tachistoscope was mounted on top of a 71 cm high table and the entire apparatus was concealed from the subjects. The rated light output of the tachistoscope was 105 lm. Room illumination was measured at 79 cd rrf2. 3.1.4 Design and procedure. The design and procedure were identical to those employed in experiment 1 with the exception that the instructions were modified to read 'small black X' rather than 'tone'. 3.2 Results and discussion For each experimental condition, the data were averaged across subjects by computing the geometric means of the estimates for each presentation interval. Straight lines were fitted by regression analysis to the logarithmic duration estimates as a function of the logarithm of physical duration as shown in figure 2; the slopes, .y-intercepts, F-values from the regression analyses, and correlation coefficients are shown in table 1. As in experiment 1, a nearly direct and linear function adequately describes the relationship between judged duration and physical duration. In both conditions where a standard stimulus was not provided, judged duration was a slightly decelerating function of physical duration, while in both conditions with a standard, judged duration was a slightly accelerating function of physical duration. Although others (Goldstone et al 1959) have found that a standard may exert a greater influence on the judged duration of a visual stimulus than on the judged duration of an auditory one, this same trend evident in the present study was not significant [F(3, 36) = 1-63; the analysis of variance was based on the individual slopes per method of estimation, as shown in table 3]. In order to compare the effects of stimulus modality, individual duration estimates between modalities, but within each method of instruction, were examined. The fact that the two power functions in each method were nearly parallel, i.e. their slopes were approximately equal, indicates no interaction of physical duration by stimulus modality. Hence a t test was performed on the difference between the mean duration estimates for visual and auditory stimuli for each of the two methods of instruction without a standard stimulus. (No difference between estimates is expected in the standard-stimulus conditions, since its use serves to equate the intercepts of the functions.) Although there was a clear trend for auditory intervals to be judged 2-2 1-8
|-
1-4 •2
1-0 0-60 0-20 -0-20
magnitude estimation with modulus — magnitude estimation verbal estimation verbal estimation with modulus
-0-60
-0-60
-0-20 0 0-20 0-60 Physical duration (lg s) Figure 2. Logarithmic plots of duration estimates by physical duration for four experimental tasks. Intervals were defined by duration of a visual target.
708
D J Bobko, J G Thompson, H R Schiffman I
longer than physically equal intervals defined by a visual stimulus (see ^-intercepts in table 1), no significant differences were found between modalities. This result does not lend support to findings by previous researchers that auditory intervals are judged longer than visually defined intervals; however, it should be noted that the differences between estimates for auditory stimuli and visual stimuli reported in several earlier experiments were slight, and no significance levels were reported (see Stevens and Galanter 1957; Stevens and Greenbaum 1966). One exception to this is a study by Behar and Bevan (1961), where auditory intervals were judged to be about 20% longer than equal intervals defined by a visual stimulus, but methodological variations (category judgments vs magnitude estimates) may account for this discrepancy. Of interest also is a study by Warm et al (1975) in which duration estimates from a fractionation task were not different for the two modalities. Table 3. Individual slopes and correlation coefficients for each method of duration estimation (visual stimulus). Subject Verbal estimation
1 2 3 4 5 6 7 8 9 10
Verbal estimation with modulus
Magnitude estimation
Magnitude estimation with modulus
slope
r
slope
r
slope
r
slope
r
0-83 0-97 1-03 0-69 0-80 1-32 0-96 1-04 0-85 1-17
0-99 0-98 0-93 0-95 0-98 0-96 0-98 0-94 0-90 0-98
1-16 0-95 1-04 0-94 1-01 0-88 1-20 1-18 1-28 0-89
0-99 0-95 0-96 0-96 0-94 0-94 0-95 0-92 0-96 0-97
1-04 0-95 0-82 1-21 0-96 0-71 0-77 0-84 1-00 0-91
0-91 0-97 0-97 0-95 0-97 0-94 0-92 0-98 0-90 0-93
1-65 1-17 0-96 0-54 1-10 1-06 1-14 1-03 0-97 1-33
0-89 0-96 0-82 0-77 0-88 0-98 0-91 0-87 0-97 0-95
Clearly, the results of the present experiments indicate that a power function provides an adequate description of duration experience, at least for the stimulus intervals employed herein. Furthermore, the exponent for the function relating judged duration and physical duration is about 1 -0 for both the visual and the auditory modality; the geometric mean of the eight slopes in table 1 is 0-97 and, as Stevens and Greenbaum (1966) note, the methods of estimation tend in general to underestimate the exponent of the power function. Thus the present results tend to confirm the nearly direct and linear relationship between judged duration and physical duration reported by Stevens (1960) and Stevens and Greenbaum (1966), but are in conflict with those of Eisler (1975). In addition, the results reported here do not lend strong support to previous reports that auditory intervals are overestimated relative to intervals defined by a visual stimulus. This is interesting in light of the recent finding by Warm et al (1975) that duration estimates in a within-group design of visual and auditory intervals are apparently independent of the stimulus modality. A possible interpretation of the present results is offered by current theories of duration experience, which postulate a central mechanism that mediates duration judgments independently of the stimulus modality (Creelman 1962; Treisman 1963; Allan and Kristofferson 1974). Acknowledgements. This research was supported by funds from the Research Council of Rutgers, The State University, Grant 07-2109, and from the Charles and Johanna Busch Memorial Fund.
The perception of brief temporal intervals
709
References Allan L, Kristofferson A, 1974 "Psychophysical theories of duration discrimination" Perception and Psychophysics 16 26-34 Behar I, Bevan W, 1961 "The perceived duration of auditory and visual intervals: cross-modality comparisons and interactions" American Journal of Psychology 74 17-26 Creelman C D, 1962 "Human discrimination of auditory duration" Journal of the Acoustical Society of America 34 582-593 Eisler H, 1975 "Subjective duration and psychophysics" Psychological Review 82 429-450 Goldstone S, Boardman W K, Lhamon W T, 1959 "Intersensory comparisons of temporal judgments" Journal of Experimental Psychology 57 243-249 Goldfarb J L, Goldstone S, 1964 "Properties of sound and audio-visual difference in time judgment" Perceptual and Motor Skills 19 606 Stevens S S, 1960 "The psychophysics of sensory function" American Scientist 48 226-253 Stevens S S, 1971 "Issues in psychophysical measurement" Psychological Review 78 426-450 Stevens S S, Galanter E H, 1957 "Ratio scales and category scales for a dozen perceptual continua" Journal of Experimental Psychology 54 377-411 Stevens S S, Greenbaum H B, 1966 "Regression effect in psychophysical judgment" Perception and Psychophysics 1 439-446 Treisman M, 1963 "Temporal discrimination and the indifference interval: implications for a model of the 'internal clock'" Psychological Monographs 11 1-31 Warm J S, Stutz R M, Vassolo P A, 1975 "Intermodal transfer in temporal discrimination" Perception and Psychophysics 18 281-286
The perception of brief temporal intervals: power functions for auditory and visual stimulus intervals
Douglas J Bobko, Jack G Thompson, Harvey R Schiffman Department of Psychology, Rutgers, The State University, New Brunswick, New Jersey 08903, USA Received 25 January 1977
Abstract. Two experiments were performed to examine the role of method of estimation and the employment of a standard stimulus on the judged duration of auditory and visual stimuli presented for brief temporal intervals (0-25 to 5-0 s). The results indicate that the relationship between judged and physical duration is nearly direct and linear. Psychophysical methodology and stimulus modality exerted little influence on the obtained power functions. 1 Introduction Stevens and Galanter (1957) proposed that the relationship between the judged and the physical duration of a stimulus presentation is best described by a power function, i.e. duration belongs to the class of prothetic continua. However, empirical evidence concerning the value of the power function exponent is sparse and equivocal. Stevens (1960) and Stevens and Greenbaum (1966) reported that the judged duration of white noise within the range of 0-30-50-0 s is "almost a linear but slightly accelerating function of physical duration" (exponent of about 1-1). That is, judged duration increases at a slightly faster rate than physical increments. Eisler (1975), on the other hand, found the converse relationship: Judged duration is a decelerating function of physical duration, with an exponent of about 0 • 84 for auditory intervals ranging from 1-3-20-0 s. Accordingly, the present study was performed to assess the nature of the power function relating judged and physical duration by presenting a pure tone of fixed intensity for brief temporal intervals. Additionally, four different sets of instructions (verbal estimation and magnitude estimation, each with and without a standard stimulus) were employed to investigate the role of psychophysical methodology and the role of a standard stimulus on duration judgments. Although Stevens (1971) has argued that the use of a standard stimulus is unnecessary for many sensory-perceptual continua, there is a lack of empirical data on the effects of such manipulations in duration judgments. Theoretically, differences in the choice of a standard stimulus should effect changes in the intercept of the power function but not in the slope (Stevens 1971). Of subsidiary interest were possible differences in the psychophysical duration functions which result either from a well-practiced and familiar response language, e.g. direct verbal estimation in seconds, or a standard magnitude estimation procedure. 2 Experiment 1 2.1 Method 2.1.1 Subjects. Forty volunteers from an introductory course in psychology served as subjects. 2.1.2 Stimuli. The stimuli were twenty time intervals, ranging from 0-25 to 5-0 s in equal steps of 0 • 25 s. The stimulus intervals were defined by the onset and termination of a pure 1500 Hz tone. The intensity of the tone was measured at 35 dB (the reference level was 0-0002 /zbar).
704
D J Bobko, J G Thompson, H R Schiffman
2.1.3 Apparatus. The main testing apparatus consisted of a Sine Wave Generator (Dynascan, model E 31 OB), headphones, and a silent-running timer (Hunter, model 11 IB). The apparatus was concealed from the subjects. 2.1.4 Design and procedure. Four different psychophysical tasks were employed: (i) verbal estimation, (ii) verbal estimation with a standard stimulus, (iii) direct magnitude estimation, and (iv) magnitude estimation with a standard stimulus. In the two verbal-estimation conditions the subjects' task was to estimate the duration of each interval in seconds and fractions of a second, while in the magnitudeestimation tasks subjects were instructed to assign a numerical value to each interval to indicate its length. In both conditions with a standard stimulus, the first interval presented during testing was fixed at 2-5 s and served as the standard; in the verbalestimation-with-standard-stimulus condition the subjects were informed of the actual duration of the standard interval in seconds, while in the magnitude-estimation-withstandard-stimulus condition the subjects were instructed to assign the interval a value of 100. A between-groups design was employed. Ten subjects were randomly assigned to each of the four experimental conditions (instructions). Except for the instructions, the procedure was identical for all subjects. The subjects were seated in front of the apparatus, and their wristwatches were removed. Subjects assigned to the verbal-estimation conditions were read the following instructions: "This is an experiment on time perception. A tone will be presented for different intervals of time. I want you to estimate how long you think the tone is on for during each interval to the nearest second and fraction of a second. (i) Try to estimate the first interval as accurately as you can in seconds and fractions of a second. Thereafter try to keep your judgments proportional. For example, if you think that the first interval is 2 • 5 s long, any interval that you think is twice as long should be called 5 s, and any interval you think is half as long should be called 1 • 25 s. (ii) I am going to present the tone for 2-5 s for the first interval. Thereafter try to keep your judgments proportional. For example, any interval that you think is twice as long should be called 5 s, and any interval you think is half as long should be called 1-25 s. Please do not count or tap during the experiment. Do you have any questions?" Subjects assigned to the magnitude-estimation conditions were read the following instructions: "This is an experiment on time perception. A tone will be presented for different intervals of time. I want you to estimate how long you think the tone is on for during each interval in relation to the first interval. (iii) Choose any convenient and reasonable number to stand for the first time interval. Thereafter try to keep your judgments proportional. For example, if you think that any interval is twice as long as the first interval you should assign it a number twice as large. Any interval that you think is half as long as the first interval should be assigned a number half the value of the first interval. (iv) I am going to present the first tone for an interval length which you should call 100. Thereafter try to keep your judgments proportional. For example, any interval that you think is twice as long as the first interval should be called 200, and any interval you think is half as long should be called 50. Please do not count or tap during the experiment. Do you have any questions?"
The perception of brief temporal intervals
705
In the standard-stimulus conditions the standard tone of 2-5 s was presented first; then the tone was presented for the twenty time intervals. All intervals were presented to each subject in random order and different randomized orders were employed for each subject. The interstimulus interval was approximately 20 s, during which the subjects estimated the duration of the stimulus presentation. Room illumination was measured at 79 cd m~2. 2.2 Results and discussion For each experimental condition, the data were averaged across subjects by computing the geometric mean of the estimates for each presentation interval. Straight lines were fitted by regression analysis to the logarithms of duration estimates as a function of the logarithm of physical duration as shown in figure 1; the slopes, ^-intercepts, correlation coefficients, and F-values from the regression analyses are shown in table 1. The significant F values (each at p < 0-01) and corresponding high correlation coefficients suggest that the relationship between the logarithm of judged duration and the logarithm of physical duration is linear and thus conforms to a power function; also, since the exponents of the power functions are close to 1-0, the function relating judged and physical duration may simply be described as a nearly direct and linear one. In all four experimental conditions, judged duration is a slightly decelerating function of physical duration. In order to test whether the instructions significantly affected the subjects' judgments, a regression analysis was 2-2
1-8 1-4 1-0 0-60 0-20 -0-20
magnitude estimation with modulus magnitude estimation verbal estimation verbal estimation with modulus
-0-60
JL_
_L_
J
-0-20 0 0-20 0-60 Physical duration (lg s) Figure 1. Logarithmic plots of duration estimates by physical duration for four experimental tasks. Duration intervals were defined by a 1500 Hz tone. -0-60
Table 1. Power-function slopes, intercepts, correlation coefficients, and F-values by method of estimation for auditory and visual stimuli. Method
Slope
Correlation coefficient F(l,18)
Intercept
auditory visual auditory visual auditory Verbal estimation Verbal estimation with modulus Magnitude estimation Magnitude estimation with modulus Geometric mean
visual
auditory visual
0-95 0-90
0-98 1-03
0-24 0-0
0-07 -0-06
0-992 0-994
0-995 0-968
1142-63 1796-08 1379-52 267-10
0-92 0-99
0-91 1-09
0-85 1-59
0-45 1-46
0-982 0-995
0-983 0-986
484-81 1827-78
0-94
1-00
518-33 608-37
706
D J Bobko, J G Thompson, H R Schiffman
performed on each subject's estimates (lg units) and an analysis of variance was performed on the resulting exponents. (The slopes and correlation coefficients for each subject are shown in table 2.) The main effects due to instructions were not significant [F(3, 36) = 1-14]. This suggests that under the present conditions of testing, the methods of verbal and direct magnitude estimation and the presence or absence of a standard stimulus exert little influence on the subjects' judgments. It is of interest also to note that the slopes of the power functions varied considerably between subjects; the exponents ranged from 0-63 to 1-46. It should be emphasized that this is not an uncommon finding even when each subject makes several estimates per stimulus interval (see Eisler 1975, p 446). Indeed, Stevens (1960) notes that an exponent based on group data "... represents an average value and is not necessarily appropriate to a particular individual" (p 236). A number of researchers (Goldstone et al 1959; Behar and Bevan 1961; Goldfarb and Goldstone 1964; Stevens and Greenbaum 1966) have reported that the judged duration of a stimulus is affected by the stimulus modality employed. Specifically, a given interval defined by a visual stimulus is judged relatively shorter than an interval of equal duration defined by an auditory stimulus. Accordingly, experiment 2 was designed to investigate this phenomenon by substituting a visual target for the auditory stimulus employed in experiment 1. Since the stimulus intervals used were identical to those of the previous study, any difference in duration estimates between modalities, and for a given instructional set, should be manifest in a difference of the power function intercepts. That is to say, if an auditory-stimulus duration appears longer than a physically equal duration of a visual stimulus, then the numerical values assigned to the auditory stimuli should be larger than those assigned to equivalent visual stimuli. Table 2. Individual slopes and correlation coefficients for each method of duration estimation (auditory stimulus). Subject Verbal estimation
1 2 3 4 5 6 7 8 9 10
Verbal estimation with modulus
Magnitude estimation
Magnitude estimation with modulus
slope
r
slope
r
slope'
r
slope
r
1-11 0-99 0-97 0-83 0-97 0-91 0-86 0-84 0-63 0-87
0-95 0-99 0-98 0-89 0-91 0-97 0-94 0-92 0-77 0-94
0-75 1-46 0-80 0-88 0-97 0-93 0-87 1-02 0-73 0-98
0-96 0-96 0-96 0-97 0-96 0-96 0-98 0-84 0-95 0-97
1-07 1-08 0-92 0-76 1-01 1-01 1-32 1-06 0-79 1-05
0-93 0-98 0-97 0-94 0-98 0-98 0-95 0-96 0-96 0-92
0-97 0-93 0-66 0-65 0-85 0-96 0-92 0-82 1-22 0-82
0-97 0-96 0-94 0-93 0-98 0-96 0-97 0-96 0-97 0-97
3 Experiment 2 3.1 Method 3.1.1 Subjects. Forty volunteers from the same population as the subjects in experiment 1 served as subjects. 3.1.2 Stimuli. The stimuli were the twenty time intervals employed in experiment 1. A small black 'X' subtending a visual angle of 1°14' served as the stimulus target. The target was constructed from 1 • 5 mm wide black graph tape mounted on a card of white poster board. During the testing, the midpoint of the target was congruent with the center of the presentation field.
The perception of brief temporal intervals
707
3.1.3 Apparatus. The main testing apparatus was a two-channel tachistoscope (Gergrands, model TIC). The tachistoscope was mounted on top of a 71 cm high table and the entire apparatus was concealed from the subjects. The rated light output of the tachistoscope was 105 lm. Room illumination was measured at 79 cd rrf2. 3.1.4 Design and procedure. The design and procedure were identical to those employed in experiment 1 with the exception that the instructions were modified to read 'small black X' rather than 'tone'. 3.2 Results and discussion For each experimental condition, the data were averaged across subjects by computing the geometric means of the estimates for each presentation interval. Straight lines were fitted by regression analysis to the logarithmic duration estimates as a function of the logarithm of physical duration as shown in figure 2; the slopes, .y-intercepts, F-values from the regression analyses, and correlation coefficients are shown in table 1. As in experiment 1, a nearly direct and linear function adequately describes the relationship between judged duration and physical duration. In both conditions where a standard stimulus was not provided, judged duration was a slightly decelerating function of physical duration, while in both conditions with a standard, judged duration was a slightly accelerating function of physical duration. Although others (Goldstone et al 1959) have found that a standard may exert a greater influence on the judged duration of a visual stimulus than on the judged duration of an auditory one, this same trend evident in the present study was not significant [F(3, 36) = 1-63; the analysis of variance was based on the individual slopes per method of estimation, as shown in table 3]. In order to compare the effects of stimulus modality, individual duration estimates between modalities, but within each method of instruction, were examined. The fact that the two power functions in each method were nearly parallel, i.e. their slopes were approximately equal, indicates no interaction of physical duration by stimulus modality. Hence a t test was performed on the difference between the mean duration estimates for visual and auditory stimuli for each of the two methods of instruction without a standard stimulus. (No difference between estimates is expected in the standard-stimulus conditions, since its use serves to equate the intercepts of the functions.) Although there was a clear trend for auditory intervals to be judged 2-2 1-8
|-
1-4 •2
1-0 0-60 0-20 -0-20
magnitude estimation with modulus — magnitude estimation verbal estimation verbal estimation with modulus
-0-60
-0-60
-0-20 0 0-20 0-60 Physical duration (lg s) Figure 2. Logarithmic plots of duration estimates by physical duration for four experimental tasks. Intervals were defined by duration of a visual target.
708
D J Bobko, J G Thompson, H R Schiffman I
longer than physically equal intervals defined by a visual stimulus (see ^-intercepts in table 1), no significant differences were found between modalities. This result does not lend support to findings by previous researchers that auditory intervals are judged longer than visually defined intervals; however, it should be noted that the differences between estimates for auditory stimuli and visual stimuli reported in several earlier experiments were slight, and no significance levels were reported (see Stevens and Galanter 1957; Stevens and Greenbaum 1966). One exception to this is a study by Behar and Bevan (1961), where auditory intervals were judged to be about 20% longer than equal intervals defined by a visual stimulus, but methodological variations (category judgments vs magnitude estimates) may account for this discrepancy. Of interest also is a study by Warm et al (1975) in which duration estimates from a fractionation task were not different for the two modalities. Table 3. Individual slopes and correlation coefficients for each method of duration estimation (visual stimulus). Subject Verbal estimation
1 2 3 4 5 6 7 8 9 10
Verbal estimation with modulus
Magnitude estimation
Magnitude estimation with modulus
slope
r
slope
r
slope
r
slope
r
0-83 0-97 1-03 0-69 0-80 1-32 0-96 1-04 0-85 1-17
0-99 0-98 0-93 0-95 0-98 0-96 0-98 0-94 0-90 0-98
1-16 0-95 1-04 0-94 1-01 0-88 1-20 1-18 1-28 0-89
0-99 0-95 0-96 0-96 0-94 0-94 0-95 0-92 0-96 0-97
1-04 0-95 0-82 1-21 0-96 0-71 0-77 0-84 1-00 0-91
0-91 0-97 0-97 0-95 0-97 0-94 0-92 0-98 0-90 0-93
1-65 1-17 0-96 0-54 1-10 1-06 1-14 1-03 0-97 1-33
0-89 0-96 0-82 0-77 0-88 0-98 0-91 0-87 0-97 0-95
Clearly, the results of the present experiments indicate that a power function provides an adequate description of duration experience, at least for the stimulus intervals employed herein. Furthermore, the exponent for the function relating judged duration and physical duration is about 1 -0 for both the visual and the auditory modality; the geometric mean of the eight slopes in table 1 is 0-97 and, as Stevens and Greenbaum (1966) note, the methods of estimation tend in general to underestimate the exponent of the power function. Thus the present results tend to confirm the nearly direct and linear relationship between judged duration and physical duration reported by Stevens (1960) and Stevens and Greenbaum (1966), but are in conflict with those of Eisler (1975). In addition, the results reported here do not lend strong support to previous reports that auditory intervals are overestimated relative to intervals defined by a visual stimulus. This is interesting in light of the recent finding by Warm et al (1975) that duration estimates in a within-group design of visual and auditory intervals are apparently independent of the stimulus modality. A possible interpretation of the present results is offered by current theories of duration experience, which postulate a central mechanism that mediates duration judgments independently of the stimulus modality (Creelman 1962; Treisman 1963; Allan and Kristofferson 1974). Acknowledgements. This research was supported by funds from the Research Council of Rutgers, The State University, Grant 07-2109, and from the Charles and Johanna Busch Memorial Fund.
The perception of brief temporal intervals
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References Allan L, Kristofferson A, 1974 "Psychophysical theories of duration discrimination" Perception and Psychophysics 16 26-34 Behar I, Bevan W, 1961 "The perceived duration of auditory and visual intervals: cross-modality comparisons and interactions" American Journal of Psychology 74 17-26 Creelman C D, 1962 "Human discrimination of auditory duration" Journal of the Acoustical Society of America 34 582-593 Eisler H, 1975 "Subjective duration and psychophysics" Psychological Review 82 429-450 Goldstone S, Boardman W K, Lhamon W T, 1959 "Intersensory comparisons of temporal judgments" Journal of Experimental Psychology 57 243-249 Goldfarb J L, Goldstone S, 1964 "Properties of sound and audio-visual difference in time judgment" Perceptual and Motor Skills 19 606 Stevens S S, 1960 "The psychophysics of sensory function" American Scientist 48 226-253 Stevens S S, 1971 "Issues in psychophysical measurement" Psychological Review 78 426-450 Stevens S S, Galanter E H, 1957 "Ratio scales and category scales for a dozen perceptual continua" Journal of Experimental Psychology 54 377-411 Stevens S S, Greenbaum H B, 1966 "Regression effect in psychophysical judgment" Perception and Psychophysics 1 439-446 Treisman M, 1963 "Temporal discrimination and the indifference interval: implications for a model of the 'internal clock'" Psychological Monographs 11 1-31 Warm J S, Stutz R M, Vassolo P A, 1975 "Intermodal transfer in temporal discrimination" Perception and Psychophysics 18 281-286
