# Individual Subitizing Range (ISR) calculator

Created by Tali Raveh at 2019-01-23 13:53:46, updated at 2019-01-24 09:55:22

**Short description**
A matlab code that calculates subitizing range at the individual level based on response times from vocal enumeration task.
The OSF link includes the code, a readMe file and a child-friendly OpenSesame vocal enumeration task.

**Reference**
Leibovich-Raveh, T., Lewis, D. J., Al-Rubaiey Kadhim, S., & Ansari, D. (2018). A New Method for Calculating Individual Subitizing Ranges. Journal of Numerical Cognition, 2018, Vol. 4(2), 429–447, https://doi.org/10.5964/jnc.v4i2.74

**Authors** Tali Leibovich-Raveh, Daniel Jacob Lewis, Saja Al-Rubaiey Kadhim, Daniel Ansari

Comment by Attila Krajcsi (2019-03-16 15:18:01, updated at 2019-03-16 15:41:20)

Support

The work provides an individual subitizing range calculation method based on sigmoid fit: First it finds the parameters of the sigmoid fit, then based on these parameters, it finds the point where tangent line crosses the x-axis, which point can be seen as an “elbow point” close to the subitizing range (see Figure 3 of the paper, displayed below).

The method seems like a reasonable extension of the sigmoid fit method, and I can imagine that this could be useful, especially, when the data show a sigmoid-like pattern.

While the paper highlights some of the advantages of the sigmoid elbow point method, and stresses that it is superior to the bilinear fit method, the paper misses to discuss some relevant features of both methods that might modulate the conclusion.

- Although the paper states that the method is a mixture of sigmoid and bilinear function, I believe that it is a purely sigmoid function fit, because it does not fit the data with linear methods. Instead, after fitting the data with a sigmoid function, a new index is created based on the found parameters. In other words, the method is a sigmoid fit method, which provides a new index instead of the former sigmoid method that purely offers the parameters of the fit.
- While the paper states that unlike the bilinear fit, the sigmoid fit does not require assumptions (such as the slope of the subitizing range is smaller than the slope of the counting range), I think the sigmoid function also have assumptions, although not in the parameters of the fit, but in the shape of the function.
- Related to the previous issue, the assumptions in the shape of the function may have their own limitations. For example, models for subitizing may suppose that the slope of the subitizing range and the slope of the counting range may be independent. Independent slopes can be measured with the bilinear fit, but they cannot be measured with the sigmoid fit, because in sigmoid fit, the slopes of both ranges depend on the same parameters (which is the consequence of the assumption of the function shape).
- It might be reasonable that a bilinear fit is more appropriate when the data do not show a plateau for large numbers (as in Figure 8 of the paper) and sigmoid function is more appropriate with a plateau for large numbers. (Note that in line with this argument the paper mostly criticizes the bilinear fit with data showing a plateau on Figure 1.) Note that the paper does not contrast empirically the bilinear and the sigmoid methods, but it contrasts only the sigmoid method with the parameters of the fit (i.e. the classic sigmoid fit) and the sigmoid version with the new index (i.e. the new method offered by the paper).

Overall, the proposed method seems to be reasonable, even if I guess some arguments exaggerate the advantages of the sigmoid method over the bilinear method. Further works could sort out the specific distinctive properties of different methods and the conditions where one or the other method could be more beneficial.

Disclaimer: I was one of the reviewers for this paper.

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