Abstract
The Approximate Number Sense (ANS) is a psychophysical construct thought to underlie quantity estimation, number processing, and the acquisition of number and math concepts during childhood. ANS acuity can be measured through speeded quantitative comparison items, which can be metricized through an “internal Weber fraction”, w, of an individual’s sensitivity to numerical differences. An individual’s w is a latent trait with two associated item models, which are uniquely grounded in psychophysical theory and modern neuroscience research: least squares error and maximum likelihood estimation. However, researchers interested in the ANS have overlooked the utility of IRT modeling for estimating w. We leverage over 30,000 job applicants through the pymetrics job matching platform, which includes a common ANS assessment, to compare and relate the parameters, fit and predictions of psychophysical models to “ordinary” IRT models.
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Notes
- 1.
Although Dietrich et al. (2016) give the logarithm in Equation 3 as base 2, w estimated using that base differ from the linear model by a constant scale factor. Dehaene (2007) does not specify a logarithm base, but his footnote 1 implies natural logarithm, which gives a much closer match to the linear model.
- 2.
Pymetrics operates on voluntary data only, and as such demographic information is limited by applicant disclosure.
- 3.
This boundary might be considered a ceiling, as it is the upper limit of w; however, as high values of w go with poor performance, low ability, and low scores on traditional scales, we think of it as a performance floor.
- 4.
In anticipation of more involved future research, the authors implemented the calibration and scoring algorithm as a Java application, in lieu of using any of several publicly available estimation packages which would likely have sufficed for the current study.
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Acknowledgements
We would like to thank Frida Polli, founder of pymetrics. We would also like to thank Su Mei Lee for her work on the development of Magnitudes and the adaptation of the least-squares scoring algorithm, and Fedor Garin and Zachary Smith for leading the front-end design of the Magnitudes app. Finally, we would like to thank David Thissen and Dylan Molenaar for helpful comments on earlier drafts.
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Thissen-Roe, A., Baker, L. (2021). Estimating Approximate Number Sense (ANS) Acuity. In: Wiberg, M., Molenaar, D., González, J., Böckenholt, U., Kim, JS. (eds) Quantitative Psychology. IMPS 2020. Springer Proceedings in Mathematics & Statistics, vol 353. Springer, Cham. https://doi.org/10.1007/978-3-030-74772-5_8
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