Comments on current ratio-setting models for time perception

Abstract

This paper is concerned with the analysis and interpretation of ratio-setting data. Ratiosetting data have been used in support of the conclusion that time perception is not veridical. In the present paper, new ratio-setting data are presented and it is argued that the existing ratio-setting models do not allow the psychophysical law for time to be derived. Eisler (1976) has recently published an impressive survey of III time perception studies employing the methods of ratio-setting and/or magnitude estimation. He concluded that time perception is not veridical, and that the psychophysical function relating subjective (internal) time to stimulus time is best described by the power law. He found that although the exponents estimated from these studies straddled unity, most were less than 1.00, and he concluded that, on the average, the exponent for time is about .90.In conflict with Eisler's conclusion that subjective time is a power function of stimulus time are the discrimination data which suggest that subjective time is a linear function of stimulus time. Many of the quantitative models for human duration discrimination assume that repeated presentation of the same stimulus duration results in a distribution of internal duration values. The models proposed by Allan and Kristofferson (1974), Creelman (1962), Getty (1975, and Kinchla (1972) differ regarding the form of the distribution and the relationship between the variance of the distribution and stimulus duration, but are similar in that the expected value of the distribution is a linear function of stimulus duration. (It should be noted that Getty's model is consistent with both a linear and a logarithmic relationship between the expected value and stimulus duration, but not with a power relationship). Kristofferson (1977) has shown that under some circumstances duration discrimination can be interpreted as temporal order discrimination. His data are compatible with a model which places all of the This research was supported by Grant A8260 from the National Research Council of Canada. The paper was written while I was on sabbatical at the University of Stirling, Stirling, Scotland. I would like to express my appreciation to the Psychology Deparment for providing a conducive atmosphere for scholarship. Requests for reprints should be sent to Lorraine G. Allan, Psychology Department, McMaster University, Hamilton, Ontario, L8S 4KI, Canada. variability in the criterion and none in the stimulus. This model, the real-time criterion model, states that there is no transformation of stimulus time into psychological time. Subjective time is real time.Perhaps the most important difference between the ratio-setting literature and the duration discrimination literature is the model used to make inferences about the psychophysical law. The duration discrimination models are at least two-parameter models. There are always a discrimination parameter and a response bias or criterion parameter. The ratio-setting models proposed by Eisler (1975) and Ekman (1958, Note 1) ar...

The parallel-clock model: Replies to critics and criticisms

“…Assuming the latter to be the case, an exponent of .80 is obtained, in excellent agreement with the two exponents deriving from reproduction (.81 and .74). The same relapse phenomenon seems to have occurred with one or two of my observers in their halving task (Eisler, 1975, Table 5, Observer 3 and possibly Observer 10), thereby explaining the low correlation of .14 between the exponents obtained from reproduction and halving over 12 observers, a result mentioned by Allan (1978Allan ( , 1979. Since observers when relapsing typically do so into easier, rather than more difficult, tasks,' I judge this finding as highly supportive of the PC model in general and of the null-instrument analogy in particular.…”

“…Whereas this observer's exponent from reproduction is about .78, doubling yielded an exponent of only .47. However, Figure 2 in Allan (1978) clearly demonstrates that S. K.'s data for the two reproduction tasks and the doubling task coincide within random errors. In this situation, one has the choice of considering the PC model invalid-or of assuming that the observer, rather than following a difficult instruction, relapses into an easier task, reproduction.…”

“…In a recent comment, Allan (1978) contested the finding (Eisler, 1975(Eisler, , 1976) that time perception, rather than being veridical, follows a power function with an exponent of about .9. She bases her conclusion on diverse findings from earlier durationdiscrimination studies, on Kristofferson's (1977) realtime criterion model, and on lack of invariance of the exponent of the power function of duration obtained from ratio-setting data.…”

“…The doubling data from Allan's (1978) observer S. K. constitute an interesting case. Whereas this observer's exponent from reproduction is about .78, doubling yielded an exponent of only .47.…”

The role of succession in temporal cognition: Is the time-order error a recency effect of memory?

“…In our experiments, subjects were presented with two intervals on each trial and were required to reproduce either the first or second interval. Given the ample evidence in the literature supporting a linear relationship between physical and reproduced time (see, e.g., Allan, 1978), we reasoned that if the TOE was due to sensitivity, then a difference should obtain between the slopes of the regression lines fit to reproductions of intervals presented first and second. To calculate meaningful regression functions, however, one requires judgments over a range of intervals.…”