Abstract
Tse et al. (Percept Psychophys 66:1171–1189, 2004) reported that participants tend to overestimate the duration of an oddball stimulus. The size of this effect was much larger than the one reported by Ulrich et al. (Psychol Res 70:77–87, 2006). More crucially, the effect in the study of Tse et al. already emerged at short standard durations, arguing against the arousal account proposed by Ulrich et al. This study investigated whether the oddball effect reported by Tse et al. was inflated by an asymmetry effect, that is, by an asymmetrical distribution of physical comparison durations around the duration of the standard. Experiment 1 demonstrated that an asymmetry effect could mimic an oddball effect. Therefore, we conducted Experiment 2 to replicate the results by Tse et al. employing not only their original procedure but also an adaptive procedure that rather avoids an asymmetry effect. Both psychophysical procedures in this experiment revealed an oddball effect, which, however, was of smaller size than the one reported by Tse et al. Furthermore, this effect emerged only at longer standard durations, which is in agreement with the arousal account as the underlying mechanism of this robust temporal illusion.
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Notes
We did not perform statistical analyses on TE because averaging the observed TEs would already introduce a bias. For example, assume that the PSE of two observers are 80 and 120 ms for a standard duration of 100 ms. Hence, the average CE for these two observers would be zero. By contrast assume that we average their TEs instead of their CEs, that is, (100/80 + 100/120)/2 = 25/24 > 1. Thus, the average CE is zero, the average TE would be larger than one. In fact, this bias would generally apply as can be seen by using Jensen’s inequality. Let x i denote the PSE for participant i (i = 1…n) and note that the TE can be written as
\( f\left( {x_{i} } \right) = \frac{S}{{x_{i} }} \)
with S denoting the standard duration. This function is convex in the interval (0, ∞) and for convex functions Jensen’s inequality states that
\( \frac{{\sum\limits_{i = 1}^{n} {f(x_{i} )} }}{n} \ge f\left( {\frac{{\sum\limits_{i = 1}^{n} {x_{i} } }}{n}} \right) \)
and hence
\( \frac{{\sum\limits_{i = 1}^{n} {\frac{S}{{x_{i} }}} }}{n} \ge \frac{S}{{{\raise0.7ex\hbox{${\sum\limits_{i = 1}^{n} {x_{i} } }$} \!\mathord{\left/ {\vphantom {{\sum\limits_{i = 1}^{n} {x_{i} } } n}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$n$}}}}. \)
Thus, the mean TE for n participants is always larger than the TE of the mean PSE for n participants. As a consequence, averaging the TE introduces a bias that can mimic an overall oddball effect. We therefore only report the overall TEs as the standard duration divided by the mean PSE but do not perform an ANOVA on them.
These values are actually ideal. The actual standard durations employed in the experiment had to be in accordance with the refresh rate of the computer screen and were actually 73.3, 120, 193.3, 306.7, 493.3, 786.7, 1,253.3 and 2,000 ms. For the sake of clarity, however, we will use the ideal values in the main text. In general, we round all durations in the text to the nearest millisecond. .
The following values give the standard duration and in parentheses the corresponding comparison durations: 75 (33, 47, 60, 73, 87, 100, 113, 127, 140), 120 (40, 53, 67, 80, 93, 107, 120, 133, 147), 192 (33, 60, 87, 113, 140, 167, 193, 220, 247), 306 (67, 107, 147, 187, 227, 267, 307, 347, 387), 490 (213, 260, 307, 353, 400, 447, 493, 540, 587), 783 (347, 420, 493, 567, 640, 713, 787, 860, 933), 1,251 (813, 887, 960, 1,033, 1,107, 1,180, 1,253, 1,327, 1,400), and 2,000 (1,080, 1,233, 1,386, 1,540, 1,693, 1,847, 2,000, 2,153, 2,307). The comparison durations were chosen both to resemble the pattern of the values used by Tse et al. (2004) and to be compatible with the 150-Hz refresh rate of the monitor.
A separate ANOVA was performed on DL. As one should expect according to Weber’s law, DL increased with standard duration, F(7, 63) = 54.11, p < 0.001. The mean Weber fraction was 0.11 and this figure is consistent with the ones reported in the literature (e.g., Goodfellow, 1934; Grondin, 2001). Neither the main effect of procedure, F(1,9) = 0.16, p = 0.700, nor the interaction of the two factors, F(7,63) = 0.42, p = 0.732, were significant.
We conducted a third experiment (standard durations: 192, 783, and 1,251 ms), that further supports the robustness of the oddball effect. In this experiment (n = 12) the oddball was physically smaller than the standard. Specifically, this stimulus was a small stationary circle whereas the standards were stationary circles of a larger size. Since previous work (e.g., Long & Beaton, 1980; Thomas & Cantor, 1975) has shown that perceived duration increases with object size, it is possible that the effect observed in Experiment 1 and 2 is due to object size rather than to oddness. If this is the case, the effect should be eliminated or even be reversed in this experiment. However, the opposite pattern of results was found. Like in Experiment 2, CE increased with standard duration F(2,22) = 6.06, p = 0.022, and was significantly smaller than zero for standard durations of 786 and 1,251 ms (p’s < 0.05, two-tailed) but not for 192 ms. The temporal expansion factors were 1.00, 1.06 and 1.11 for standard durations of 192, 783, and 1,251 ms, respectively. This result replicates the finding from Tse et al. (2004) and from Experiment 2 that participants judge the duration of the oddball longer than the one of the standard, at least, when the duration of the standard is sufficiently long. We acknowledge that Tse et al. (2004) have already demonstrated the confounding effect of stimulus size to be rather unlikely. In their Experiment 2 they reversed oddball and standard stimulus, so that the oddball was of smaller size than the initial radius of the expanding standard. In this experiment and also with auditory stimuli, they still were able to reveal an oddball effect. Our third experiment, however, broadens the database for visual stimuli by reaffirming the oddball effect for small stationary oddballs compared to larger stationary standard stimuli.
References
Brainard, S. W. (1997). The Psychophysics Toolbox. Spatial Vision, 10, 433–436.
Brown, S. W. (1995). Time, change, and motion: The effects of stimulus movement on temporal perception. Perception & Psychophysics, 57, 105–116.
Bush, R. R. (1963). Estimation and evaluation. In L. R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 1, pp. 429–469). New York: Wiley.
Cousineau, D. (2007). Confidence intervals in within-subjects designs: A simpler solution to Loftus and Masson’s method. Tutorials in Quantitative Methods for Psychology, 1, 42–45.
Doughty, J. M. (1949). The effect of psychophysical method and context on pitch and loudness functions. Journal of Experimental Psychology, 39, 729–745.
Enns, J. T., Brehaut, J. C., & Shore, D. I. (1999). The duration of a brief event in the mind’s eye. Journal of General Psychology, 126, 355–372.
Goodfellow, L. D. (1934). An empirical comparison of audition, vision, and touch in the discrimination of short intervals of time. American Journal of Psychology, 46, 243–258.
Grondin, S. (2001). Discriminating time intervals presented in sequences marked by visual signals. Perception & Psychophysics, 63, 1214–1228.
Guilford, J. P. (1954). Psychometric methods. New York: McGraw-Hill.
Kaernbach, C. (1991). Simple adaptive testing with the weighted up-down method. Perception & Psychophysics, 49, 227–229.
Lapid, E., Ulrich, R., & Rammsayer, T. (2008). On estimating the difference limen in duration discrimination tasks: A comparison of the 2AFC and the reminder task. Perception & Psychophysics, 70, 291–305.
Long, G. M., & Beaton, R. J. (1980). The contribution of visual persistence to the perceived duration of brief targets. Perception & Psychophysics, 28, 422–430.
Masin, S. C., Fanton, V., & Crestoni, L. (1988). An experimental study of the asymmetry effect in the method of constant stimuli. Psychological Research, 50, 181–182.
Mattes, S., & Ulrich, R. (1998). Directed attention prolongs the perceived duration of a brief stimulus. Perception & Psychophysics, 60, 1305–1317.
Pelli, D. G. (1997). The VideoToolbox software for visual psychophysics: transforming numbers into movies. Spatial Vision, 10, 437–442.
Penton-Voak, I. S., Edwards, H., Percival, A., & Wearden, J. H. (1996). Speeding up an internal clock in humans? Effects of click trains on subjective duration. Journal of Experimental Psychology: Animal Behavior Processes, 22, 307–320.
Rammsayer, T., & Ulrich, R. (2001). Counting models of temporal discrimination. Psychonomic Bulletin & Review, 8, 270–277.
Romero, R., & Polich, J. (1996). P3(00) habituation from auditory and visual stimuli. Physiology & Behavior, 59, 517–522.
Sokolov, E. N. (1963). Perception and the conditioned reflex. Oxford: Pergamon Press.
Sternberg, S., & Knoll, R. L. (1973). The perception of temporal order: Fundamental issues and a general model. In S. Kornblum (Ed.), Attention and Performance IV (pp. 629–685). New York: Academic Press.
Thomas, E. A. C., & Cantor, N. E. (1975). On the duality of simultaneous time and size perception. Perception & Psychophysics, 18, 44–48.
Treisman, M., Faulkner, J., Naish, P. L. N., & Brogan, D. (1990). The internal clock: Evidence for a temporal oscillator underlying time perception with some estimates of its characteristic frequency. Perception, 19, 705–743.
Treutwein, B. (1995). Adaptive psychophysical procedures. Vision Research, 35, 2503–2522.
Tse, P. U., Intriligator, J., Rivest, J., & Cavanagh, P. (2004). Attention and the subjective expansion of time. Perception & Psychophysics, 66, 1171–1189.
Ulrich, R., Nitschke, J., & Rammsayer, T. (2006). Perceived duration of expected and unexpected stimuli. Psychological Research, 70, 77–87.
Wearden, J. H., Edwards, H., Fakhri, M., & Percival, A. (1998). Why “sounds are judged longer than lights”: Application of a model of the internal clock in humans. Quarterly Journal of Experimental Psychology: Comparative and Physiological Psychology, 51b, 97–120.
Yeshurun, Y., & Marom, G. (2008). Transient spatial attention and the perceived duration of brief visual events. Visual Cognition, 16, 826–848.
Zakay, D., & Block, R. A. (1997). Temporal cognition. Current Directions in Psychological Science, 6, 12–16.
Acknowledgments
We thank Sonja Cornelsen and Agnes Mercz for their assistance in data collection. We also thank Karin Bausenhart, Einat Lapid, and two anonymous reviewers for helpful comments. This work was supported by the Deutsche Forschungsgemeinschaft (UL 116/10-1).
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Seifried, T., Ulrich, R. Does the asymmetry effect inflate the temporal expansion of odd stimuli?. Psychological Research 74, 90–98 (2010). https://doi.org/10.1007/s00426-008-0187-x
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DOI: https://doi.org/10.1007/s00426-008-0187-x