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

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.