Limits...
Numerosity estimation in visual stimuli in the absence of luminance-based cues.

Kramer P, Di Bono MG, Zorzi M - PLoS ONE (2011)

Bottom Line: Numerosity estimation is a basic preverbal ability that humans share with many animal species and that is believed to be foundational of numeracy skills.The results show that numerosity estimation need not be based on first-order spatial filtering, first-order density perception, or any other processing of luminance-based cues to numerosity.Our method can be used as an effective tool to control non-numerical variables in studies of numerosity estimation.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Psicologia Generale, Università di Padova, Padova, Italy. peter.kramer@unipd.it

ABSTRACT

Background: Numerosity estimation is a basic preverbal ability that humans share with many animal species and that is believed to be foundational of numeracy skills. It is notoriously difficult, however, to establish whether numerosity estimation is based on numerosity itself, or on one or more non-numerical cues like-in visual stimuli-spatial extent and density. Frequently, different non-numerical cues are held constant on different trials. This strategy, however, still allows numerosity estimation to be based on a combination of non-numerical cues rather than on any particular one by itself.

Methodology/principal findings: Here we introduce a novel method, based on second-order (contrast-based) visual motion, to create stimuli that exclude all first-order (luminance-based) cues to numerosity. We show that numerosities can be estimated almost as well in second-order motion as in first-order motion.

Conclusions/significance: The results show that numerosity estimation need not be based on first-order spatial filtering, first-order density perception, or any other processing of luminance-based cues to numerosity. Our method can be used as an effective tool to control non-numerical variables in studies of numerosity estimation.

Show MeSH
Numerosity estimation in first-order and second-order motion.A linear-linear plot (top panel), and a log-log plot (bottom panel), of estimated numerosity in first-order motion (filled symbols) and second-order motion (open symbols) as a function of actual numerosity (one subject was unable to do the task even in first-order motion and was excluded from the figures). Note that the error bars (representing one standard error of the mean) increase with numerosity in the linear-linear plot, but remain constant in the log-log plot. Note also, in the bottom panel, that the relationship between estimated and physical numerosity approximately follows the power law mentioned in the text: log(ψ) = n log( ϕ)+c.
© Copyright Policy
Related In: Results  -  Collection


getmorefigures.php?uid=PMC3046164&req=5

pone-0017378-g002: Numerosity estimation in first-order and second-order motion.A linear-linear plot (top panel), and a log-log plot (bottom panel), of estimated numerosity in first-order motion (filled symbols) and second-order motion (open symbols) as a function of actual numerosity (one subject was unable to do the task even in first-order motion and was excluded from the figures). Note that the error bars (representing one standard error of the mean) increase with numerosity in the linear-linear plot, but remain constant in the log-log plot. Note also, in the bottom panel, that the relationship between estimated and physical numerosity approximately follows the power law mentioned in the text: log(ψ) = n log( ϕ)+c.

Mentions: One subject was neither able to perform the task in first-order motion, nor in second-order motion, and was excluded from the group analyses. For the first-order, and second-order, motion conditions (Figure 2, filled and open symbols, respectively), standard errors increased with estimated numerosity (respectively, adjusted R2 = .90 and adjusted R2 = .81, both p<.001). Instead, for both conditions, the coefficients of variation (i.e., standard deviation/mean) of the numerosity estimates were unrelated to the estimates themselves (for both conditions R2<.01, both with coefficient means of .33). These results suggest that the standard errors increased in direct proportion to the numerosity estimates (scalar variability), which indicates that subjects were indeed estimating rather than counting [39], [40]. We confirmed that this was indeed the case, with two separate regression analyses for the first- and second-order-motion conditions, on the logarithmically transformed data. As required [13], [39], with numerosity estimation as the independent and standard error as the dependent variable, the regression slopes for the two conditions were both close to one (r = .96 and r = .93).


Numerosity estimation in visual stimuli in the absence of luminance-based cues.

Kramer P, Di Bono MG, Zorzi M - PLoS ONE (2011)

Numerosity estimation in first-order and second-order motion.A linear-linear plot (top panel), and a log-log plot (bottom panel), of estimated numerosity in first-order motion (filled symbols) and second-order motion (open symbols) as a function of actual numerosity (one subject was unable to do the task even in first-order motion and was excluded from the figures). Note that the error bars (representing one standard error of the mean) increase with numerosity in the linear-linear plot, but remain constant in the log-log plot. Note also, in the bottom panel, that the relationship between estimated and physical numerosity approximately follows the power law mentioned in the text: log(ψ) = n log( ϕ)+c.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3046164&req=5

pone-0017378-g002: Numerosity estimation in first-order and second-order motion.A linear-linear plot (top panel), and a log-log plot (bottom panel), of estimated numerosity in first-order motion (filled symbols) and second-order motion (open symbols) as a function of actual numerosity (one subject was unable to do the task even in first-order motion and was excluded from the figures). Note that the error bars (representing one standard error of the mean) increase with numerosity in the linear-linear plot, but remain constant in the log-log plot. Note also, in the bottom panel, that the relationship between estimated and physical numerosity approximately follows the power law mentioned in the text: log(ψ) = n log( ϕ)+c.
Mentions: One subject was neither able to perform the task in first-order motion, nor in second-order motion, and was excluded from the group analyses. For the first-order, and second-order, motion conditions (Figure 2, filled and open symbols, respectively), standard errors increased with estimated numerosity (respectively, adjusted R2 = .90 and adjusted R2 = .81, both p<.001). Instead, for both conditions, the coefficients of variation (i.e., standard deviation/mean) of the numerosity estimates were unrelated to the estimates themselves (for both conditions R2<.01, both with coefficient means of .33). These results suggest that the standard errors increased in direct proportion to the numerosity estimates (scalar variability), which indicates that subjects were indeed estimating rather than counting [39], [40]. We confirmed that this was indeed the case, with two separate regression analyses for the first- and second-order-motion conditions, on the logarithmically transformed data. As required [13], [39], with numerosity estimation as the independent and standard error as the dependent variable, the regression slopes for the two conditions were both close to one (r = .96 and r = .93).

Bottom Line: Numerosity estimation is a basic preverbal ability that humans share with many animal species and that is believed to be foundational of numeracy skills.The results show that numerosity estimation need not be based on first-order spatial filtering, first-order density perception, or any other processing of luminance-based cues to numerosity.Our method can be used as an effective tool to control non-numerical variables in studies of numerosity estimation.

View Article: PubMed Central - PubMed

Affiliation: Dipartimento di Psicologia Generale, Università di Padova, Padova, Italy. peter.kramer@unipd.it

ABSTRACT

Background: Numerosity estimation is a basic preverbal ability that humans share with many animal species and that is believed to be foundational of numeracy skills. It is notoriously difficult, however, to establish whether numerosity estimation is based on numerosity itself, or on one or more non-numerical cues like-in visual stimuli-spatial extent and density. Frequently, different non-numerical cues are held constant on different trials. This strategy, however, still allows numerosity estimation to be based on a combination of non-numerical cues rather than on any particular one by itself.

Methodology/principal findings: Here we introduce a novel method, based on second-order (contrast-based) visual motion, to create stimuli that exclude all first-order (luminance-based) cues to numerosity. We show that numerosities can be estimated almost as well in second-order motion as in first-order motion.

Conclusions/significance: The results show that numerosity estimation need not be based on first-order spatial filtering, first-order density perception, or any other processing of luminance-based cues to numerosity. Our method can be used as an effective tool to control non-numerical variables in studies of numerosity estimation.

Show MeSH