Numerical error monitoring

Abstract

Error monitoring has recently been discovered to have informationally rich foundations in the timing domain. Based on the common properties of magnitude-based representations, we hypothesized that judgments on the direction and the magnitude of errors would also reflect their objective counterparts in the numerosity domain. In two experiments, we presented fast sequences of "beeps" with random interstimulus intervals and asked participants to stop the sequence when they thought the target count (7, 11, or 19) had been reached. Participants then judged how close to the target they stopped the sequence, and whether their response undershot or overshot the target. Individual linear regression fits as well as the linear mixed model with a fixed effect of reproduced numerosity on confidence ratings, and participants as independent random effects on the intercept and the slope, revealed significant positive slopes for all the target numerosities. Our results suggest that humans can keep track of the direction and degree of errors in the estimation of discrete quantities, pointing at a numerical-error-monitoring ability.

Monitoring line length reproduction errors

“…Our findings showed that in the absence of explicit feedback, humans can monitor the direction of errors in their reproductions of lengths (for nearly all targets) and their confidence ratings can track the magnitude of their errors for all target lengths. Together with our previous findings which indicate that humans can better than chance guess the direction and match their confidence to the degree of errors (based on composite measure) in their temporal (Akdoğan & Balcı, 2017; see also Doenyas, Mutluer, Genç, & Balcı, 2019;Kononowicz et al, 2018) and numerical (Duyan & Balcı, 2018) reproductions and numerical estimations (Duyan & Balcı, 2019), the results of Samaha and Postle (2017) that point toward a similar ability in relation to orientation judgment errors, and given converging evidence for a general magnitude representation system in the brain (Bueti & Walsh, 2009;Walsh, 2003), we surmise that this error monitoring ability would most likely extend to other metric domains.…”

“…In such an in-parallel information processing scheme, participants can compare their estimate to the other estimate(s) that would have been made if they had relied on another process/other processes in a retrospective fashion and this comparison can inform the agent regarding the direction and magnitude of their errors. Duyan and Balcı (2018) proposed another comparison strategy in which participants would compare their current estimate of magnitude with a random sample from their long-term memory representation for that target. In fact, such a comparison strategy forms the basis of the decision stage of the Scalar Timing Theory to guide the first order timing performance (Gibbon, Church, & Meck, 1984).…”

“…However, magnitude representations inherently contain uncertainty, which results in trial-to-trial variability in the corresponding quantity estimates. Recent work showed that confidence ratings also reflect the amount of deviation from the target in the estimation of continuous magnitudes such time (Akdoğan & Balcı, 2017), numerical estimates (Duyan & Balcı, 2018, and grating orientation (Samaha & Postle, 2017). Given the plethora of findings that point to a common system for the representation of magnitudes (Martin, Wiener, & van Wassenhove, 2017;Walsh, 2003), with evidence from studies on cross-modal transfer (e.g., (Balci & Gallistel, 2006)), cross-dimension interference (Henik & Tzelgov, 1982), and neurophysiological findings that relate a common locus (i.e., intraparietal sulcus, e.g., (Bueti & Walsh, 2009)) to various magnitude-based judgments, we hypothesized that confidence ratings and error directionality judgments would also reflect objective performance in the estimation of spatial attributes such as distance.…”

“…Over four experiments with different durations and different block designs, they found that these confidence ratings and error-directionality judgments (as a composite measure) closely followed the participants' objective timing performance (i.e., parametric and directional errors). Using a numerical analogue of this task, Duyan & Balcı (2018 showed that such quantitative error-monitoring ability also extends to the numerical estimates based on counts of sequential events as well as based on counts of a simultaneously presented array of circles. Moreover, Samaha and Postle (2017) asked participants to reproduce the orientation of a briefly presented low contrast grating and obtained error monitoring ratings on each trial.…”

Error monitoring in decision‐making and timing is disrupted in autism spectrum disorder

“…Such performance monitoring is an important component of metacognition [Fleming & Dolan, ; Garofalo & Lester, ], which in decision‐making comprises both veridical error‐monitoring and confidence judgments regarding objective performance in the absence of explicit feedback [Yeung & Summerfield, ]. Importantly, recent work has shown that typically developing (TD) individuals are aware of not only their errors but also the magnitude and direction of their errors in paradigms that enable such quantitative characterizations [Akdoğan & Balcı, ; Duyan & Balcı, ]. In the present study, we combined decision‐making, timing, and error‐monitoring, which have remained as segregated research topics in ASD up until now, to take a more comprehensive approach to understanding cognitive processing in ASD in the light of recent developments in the corresponding fields.…”