Is There a Common Summary Statistical Process for Representing the Mean and Variance? A Study Using Illustrations of Familiar Items

Abstract

A number of studies revealed that our visual system can extract different types of summary statistics, such as the mean and variance, from sets of items. Although the extraction of such summary statistics has been studied well in isolation, the relationship between these statistics remains unclear. In this study, we explored this issue using an individual differences approach. Observers viewed illustrations of strawberries and lollypops varying in size or orientation and performed four tasks in a within-subject design, namely mean and variance discrimination tasks with size and orientation domains. We found that the performances in the mean and variance discrimination tasks were not correlated with each other and demonstrated that extractions of the mean and variance are mediated by different representation mechanisms. In addition, we tested the relationship between performances in size and orientation domains for each summary statistic (i.e. mean and variance) and examined whether each summary statistic has distinct processes across perceptual domains. The results illustrated that statistical summary representations of size and orientation may share a common mechanism for representing the mean and possibly for representing variance. Introspections for each observer performing the tasks were also examined and discussed.

Independent and parallel visual processing of ensemble statistics: Evidence from dual tasks

“…Only few studies have addressed one or both of these questions. In one such study, Yang, Tokita, and Ishiguchi (2018) demonstrated the lack of correlation between the perception of mean and the perception of variance. This suggests that these two statistics can be computed quite independently, even when applied to the same domain (size or orientation).…”

“…Although testing the perception of two statistics in a single precue/postcue task (Utochkin & Vostrikov, 2017) is advantageous over separate tasks (Haberman, Brady, & Alvarez, 2015;Lee et al, 2016;Yang et al, 2018) in terms of its capability to probe parallelism along with independence, an important methodological caveat can be put forward. Specifically, when a correlation between tests is estimated across participants, each data point represents an average score that does not take into account what happens in particular trials.…”

“…Finally, while previous studies have focused on testing the links either between mean and numerosity (Lee et al, 2016;Utochkin & Vostrikov, 2017) or between mean and variance (Yang et al, 2018) and used different approaches, here we tested both these links using the same approach.…”

“…For each participant, we calculated a trialby-trial correlation between an error in the mean judgment and an error in the numerosity judgment. Second, we estimated correlations across participants, like previous researchers did (e.g., Haberman, Brady, & Alvarez, 2015;Utochkin & Vostrikov, 2017;Yang et al, 2018). Specifically, we were interested in autocorrelations of each of the summary statistics under three different conditions (e.g., mean size at baseline, mean size when reported first, and mean size when reported second) and in cross-correlations between the mean and numerosity under similar conditions (e.g., mean baseline with numerosity baseline and mean when reported first with numerosity when reported first).…”

Ensemble Statistics Accessed through Proxies: Range Heuristic and Dependence on Low-Level Properties in Variability Discrimination

“…Interestingly, participants' reports of variability were also more accurate than one would expect based on their reports of mean size in a previous experiment. Solomon et al (2011) suggested that this is accounted for by some form of late decision noise in the computation of mean size, but an alternative suggestion is that participants simply use different cognitive strategies in computing the two (e.g., Yang, Tokita, & Ishiguchi, 2018).…”