Effect of Presentation Format on Judgment of Long-Range Time Intervals

Abstract

Investigations in the temporal estimation domain are quite vast in the range of milliseconds, seconds, and minutes. This study aimed to determine the psychophysical function that best describes long-range time interval estimation and evaluate the effect of numerals in duration presentation on the form of this function. Participants indicated on a line the magnitude of time intervals presented either as a number + time-unit (e.g., “9 months”; Group I), unitless numerals (e.g., “9”; Group II), or tagged future personal events (e.g., “Wedding”; Group III). The horizontal line was labeled rightward (“Very short” = >“Very long”) or leftward (“Very long” = >“Very short”) for Group I and II, but only rightward for Group III. None of the linear, power, logistic or logarithmic functions provided the best fit to the individual participant data in more than 50% of participants for any group. Individual power exponents were different only between the tagged personal events (Group III) and the other two groups. When the same analysis was repeated for the aggregated data, power functions provided a better fit than other tested functions in all groups with a difference in the power function parameters again between the tagged personal events and the other groups. A non-linear mixed effects analysis indicated a difference in the power function exponent between Group III and the other groups, but not between Group I and II. No effect of scale directionality was found in neither of the experiments in which scale direction was included as independent variable. These results suggest that the judgment of intervals in a number + time-unit presentation invoke, at least in part, processing mechanisms other than those used for time-domain. Consequently, we propose the use of event-tagged assessment for characterizing long-range interval representation. We also recommend that analyses in this field should not be restricted to aggregated data given the qualitative variation between participants.

More Later: Delay of Gratification and Thought About the Future in Children

“…As in studies with adults (Kim & Zauberman, 2009; Zauberman et al, 2009; though see Agostino et al, 2019), the relation between objective and subjective time was nonlinear and best captured by a power function (Equation ). Notably, the beta value of the power function that we obtained (.30), which captures the degree of compression in the relation between subjective and objective time, was substantially lower than that previously obtained with adults (.72; Kim & Zauberman, 2009; .75–.87; Agostino et al, 2019). There are a number of methodological differences between the future time perception task in this study and those that have been administered to adults that may account for this difference.…”

“…Moreover, the ratio of the shortest to longest delay was considerably larger in this study (1:91.25) than in both the Kim and Zauberman and Agostino et al studies (1:12). When coupled with a bounded scale for subjective judgments, such as the line bisection task of Zauberman et al (2009) and Agostino et al (2019), a large ratio of shortest to longest duration may artificially lower beta values, due to the restrictions on participant’s responses to long durations imposed by the scale. However, in this study we used an unbounded scale, mitigating this problem.…”

“…Equation has two free parameters, an exponent, beta, that captures the degree of compression in future time perception and a coefficient, alpha. While we refer to the exponent of the power function as capturing the degree of compression in future time perception, others refer to nonlinearity (Han & Takahashi, 2012; Kim & Zauberman, 2009) or to increasing deceleration (Agostino, Zana, Balci, & Claessens, 2019). The alpha parameter is a scaling factor restricted to any positive number that is responsible for the overall height of the time function (see Figure 2a).…”

“…As the beta value diminishes subjective time judgments at longer delays become increasingly compressed relative to objective time (e.g., a week away might feel like of a year away rather than only of a year); see Figure 2b for an illustration of how changes in beta affect the relation between objective and subjective time. Studies with adults have estimated the value of beta to vary within the range .72–.87, indicating a moderate time compression (Agostino et al, 2019; Kim & Zauberman, 2009).…”

The role of time estimation in decreased impatience in intertemporal choice.

“…These functions indicate a compressed-shape, concave psychophysical mapping, implying that people estimate long time intervals in a biased form such that long intervals are estimated as being shorter than estimates made by an objective unbiased observer, that is, temporal inconsistency. The mapping function based on aggregated data (β = 0.70 ± 0.06) is in the same range of compression previously registered by Kim and Zauberman (2009; β = 0.72) and Agostino et al (2019; β = 0.77).…”