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. 2011 Feb 8;21(3):200–206. doi: 10.1016/j.cub.2010.12.043

Figure 3.

Figure 3

Stochastic Stimuli Reduce Variability in Duration Judgment

(A) In the model, the distribution of estimates obtained by combining both internal and sensory cues (blue histogram and line; distributions obtained from 5000 simulated trials) is narrower and more peaked than that obtained from the internal estimate alone (orange histogram and line). The relative variability (right) is the standard deviation divided by the mean.

(B) Design for experiment 2. A static or dynamic smoothed Gaussian noise stimulus appeared continuously at fixation. Twice in each trial, a pair of circles appeared at the edge of the noise stimulus. Duration 1 was 410 or 650 ms; duration 2 (appearing 588 ms or 50 video frames later) was a multiple of this (the range of multiples was adjusted for each subject to yield a complete psychometric curve, typically 0.45–1.8). Subjects reported whether the first or the second presentation lasted longer. Static and dynamic conditions alternated in four blocks, with the order of blocks counterbalanced across subjects.

(C) Psychophysical results. Psychometric curves (n = 20) were fit by a cumulative Gaussian combined with a probability of accidentally entering an unintended response (the lapse rate, also fit to the data). The variability was defined as the reciprocal of the maximal slope of the lapse-independent psychometric curve, corresponding to the width of the Gaussian. Scatter plot and left inset: the variability during the dynamic condition was significantly lower than that during the static condition (p = 0.005, two-sided paired t test; red circles represent per-subject averages; small black circles represent each base duration for each subject; orange and blue bars in the inset are population averages for the static and dynamic conditions, respectively, with standard errors.) Middle and right insets: mean reaction times during the easiest trials were not significantly different between the static and dynamic conditions (p = 0.64), nor were the lapse rates (p = 0.73). Error bars indicate standard errors.