Temporal bisection with trial referents

Abstract

There is general agreement among the quantitative models for time (see Allan, 1998) that mean perceived time ( μ t ) is a power function of clock time with an exponent close to 1.0,and that variability in perceived time (s t ) is proportional to mean perceived time,The proportionalityconstant g is known as the Weber fraction, and the proportionality relation is often referred to as scalar variability. This scalar property between the standard deviation and the mean results in distributions of perceived time that superpose when the temporal axis is normalized with respect to the mean of the distribution. This superposition in relative time reflects a re-scaling in time, a scale-invariant error distribution for perceived time. Many psychophysical procedures have been developed for the study of time perception (see Allan, 1979Allan, , 1998. One relatively new procedure is temporal bisection. In the prototypic temporal bisection task, two referents, one short (S ) and the other long (L), are explicitly identified either by familiarizing the subject with the referents at the beginning of a block of trials (e.g., Allan, 1999;Wearden, 1991;Wearden & Ferrara, 1995Wearden, Rogers, & Thomas, 1997) or periodically throughout a block of trials (e.g., Allan & Gibbon, 1991;Penney, Allan, Meck, & Gibbon, 1998). On probe trials, a temporal interval t, S £ t £ L, is presented, and the subject is required to indicate whether t is more similar to S (R S ) or to L (R L ). Temporal bisection yields a psychometric function relating the proportion of long responses, P(R L ), to probe duration t. The value of t at which R S and R L occur with equal frequency, P(R L ) 5 0.5, is often referred to as the bisection point (T 1/2 ). One interpretation of T 1/2 is that it is the value of t that is equally confusable with S and L. For bisection, the scalar property predicts superposition of psychometric functions for all L-to-S ratios when plotted against t normalized by the bisection point (i.e., t / T 1/2 ).A number of psychophysical models for temporal bisection have been proposed. These models differ with regard to the source of the scalar variability and the nature of the decision rule for categorizing t as R L or R S . In his now classic paper on temporal bisection, derived the bisection function for a similarity ratio decision rule. For this rule, the decision to respond R S or R L is made by comparing the similarity of the perceived value of t with memories of the two referents, S and L. This comparison is based on a ratio of the similarity of t to S relative to the similarity of t to L. If that ratio is less than a criterion b, the response is R L . Gibbon combined the similarity ratio rule with two sources for scalar variability, perception or memory. In the "referent known exactly model" (RKE), he assumed no variability in the memory for the referents and placed scalar variability in the perception of the probes. In contrast, in the "stimulusThe preparation of this paper was supported by a grant to L.G.A. from the Natural Sciences ...

The Role of Parametric Assumptions in Adaptive Bayesian Estimation.

“…What is less clear is what the data say about the relation of subjective to objective time, or whether time is under-or over-estimated as opposed to veridically perceived. The same data could have arisen if β = 1 (i.e., μ(t) = t) and the assumption that S mp = μ(t mp ) is removed, implying that observers perceive duration veridically but for some reason they do not set the anchor at μ(t mp ) during the training phase (Raslear, 1985;Allan and Gerhardt, 2001;Allan, 2002a,b). And the same shift could have been caused also with μ(t) = t and by reinstating the assumption that S mp = μ(t mp ) if observers had a non-null indifference region (i.e., δ = 0) and responded with bias when undecided ( Figure 5).…”

“…Some modifications of the temporal generalization and bisection tasks turn them into paired-comparison methods, and the models discussed here apply to them too. For instance, the roving standard task of Allan and Gerhardt (2001) or Rodríguez-Gironés and Kacelnik (2001) presents in each trial a short and a long exemplar (which vary across trials) so that observers compare the test duration with the current exemplars. Similarly, the episodic temporal generalization task of Wearden and Bray (2001) presents a variable standard in each trial which is the reference for the observers' current judgment.…”

Identification and Bisection of Temporal Durations and Tone Frequencies: Common Models for Temporal and Nontemporal Stimuli.

“…Several previous studies have indeed found good superposition under a wide range of conditions (e.g. Allan, 2002b;Allan & Gerhardt, 2001;Allan & Gibbon, 1991;Penney et al, 1998Penney et al, , 2000Wearden & Bray, 2001;Wearden & Ferrara, 1996;Wearden et al, 1997) although small departures are sometimes observed (Penney et al, 1998(Penney et al, , 2000Wearden et al, 1997).…”

“…Various versions of such tasks have been employed, allowing manipulation of factors such as the memory demands of the task (e.g., Allan, 2002a;Rodriguez-Girones & Kacelnik, 2001;Wearden & Bray, 2001) or the number of times a given duration is repeated within an experiment (e.g., Allan & Gerhardt, 2001). The stimulus durations that are employed are typically short enough (less than 1 or 2 s) to prevent chronometric counting.…”

Cross-domain transfer of quantitative discriminations: Is it all a matter of proportion?

“…Allan (2002a) and Allan and Gerhardt (2001) found that the standard of comparison did not change even when the referents changed from trial to trial. Their subjects used the range of referents encountered over many trials to establish a standard that was employed on every trial, regardless of the referents given on that trial.…”