The precision of temporal judgement: milliseconds, many minutes, and beyond

Abstract

The principle that the standard deviation of estimates scales with the mean estimate, commonly known as the scalar property, is one of the most broadly accepted fundamentals of interval timing. This property is measured using the coefficient of variation (CV) calculated as the ratio between the standard deviation and the mean. In 1997, John Gibbon suggested that different time measurement mechanisms may have different levels of absolute precision, and would therefore be associated with different CVs. Here, we test this proposal by examining the CVs produced by human subjects timing a broad range of intervals (68 ms to 16.7 min). Our data reveal no evidence for multiple mechanisms, but instead show a continuous logarithmic decrease in CV as timed intervals increase. This finding joins other recent reports in demonstrating a systematic violation of the scalar property in timing data. Interestingly, the estimated CV of circadian judgements fits onto the regression of decreasing CV, suggesting a link between short interval and circadian timing mechanisms.

Figure 1

Modified from Gibbon et al. (1997a), this shows CV from a variety of different studies plotted against the target intervals. Gibbon suggests that the pattern may imply two changes or ‘jumps’ in CV, at approximately 0.1 and 1.5 s.

Figure 2

Paradigm for the reproduction task used in experiment 1. (a) During the initial presentation phase, changes in screen colour were dictated by the program, which showed a red screen for the interval that was to be timed. Subjects initiated this presentation with a keypress, and were required to release the key when it was terminated by a white screen. (b) The reproduction phase followed and was initiated when subjects depressed the response button again. They held it down for the duration that they thought had passed during presentation. In this figure, the subject overestimates the interval by a small percentage. The number reading distraction task was performed throughout the time that the screen was red or blue.

Figure 3

(a) Demonstrates the relative accuracy with which subjects produced the intervals by plotting the mean of produced durations (calculated by averaging estimates within each subject and then across subjects), against the target (solid line) intervals. (b) Shows the CV for each subject plotted against the target intervals. The grey line represents a simple logarithmic regression. The two black lines represent a two part logarithmic regression. The parameters for all three regression lines, as well as the break point between the two black regression lines, were chosen using an iterative least-squares fitting method.

Figure 4

(a) The mean estimate of within and across the subjects in experiment 1 (pluses), experiment 2 (diamonds) and experiment 3 (asterisks) is plotted against the target interval (solid line). (b) Mean coefficients of variation (averaged within and then across subjects) for experiments 1–4 are plotted against target intervals. The grey line is a simple logarithmic regression of experiment 1 (pluses). The CV of circadian timing has been added (stars). These data were taken from (Wever 1979; Gibbon et al. 1997b). It is interesting to note that the circadian CV commonly observed in free-running circadian timing fit onto the dashed extrapolation of the regression line from experiments 2 to 4.