PDF
Abstract
Subitizing is the ability to appraise a number of small quantities (up to four) rapidly and precisely. This system, however, can be impaired by distractors presented along with targets to be enumerated. To better understand whether this limitation arises in perceptual circuits or in the response selection stage, we investigated whether subitizing can endure in simultaneous comparison tasks. Participants were asked to compare the number of dots in two sets on the left and right sides of the screen, presented either simultaneously or sequentially. For comparing within the numerosity range (6–32 dots), both the error rate and reaction time increased steadily as the ratio between the two numbers compared approached “1.” Namely, a phenomenon labeled the ratio effect was revealed. For comparison with small numbers (<5), the sequential comparison task was errorless despite the ratio, suggesting the feature of subitizing. Individual efficiency (measured by the inverse efficiency score [IES]) did not correlate between number ranges in sequential comparison, suggesting that distinct mechanisms were involved. However, we found that in simultaneous tasks, error rate and efficiency showed an increase as the ratios of the two numbers compared approached “1.” This is similar to the ratio effect revealed in the comparison for moderate numbers. Individual efficiency within these two ranges correlated, indicating that the enumeration within these two ranges was based on a single mechanism. These results suggest that subitizing cannot process sets in parallel, and numerosity takes the job whenever subitizing fails.
Keywords
estimation
/
inverse efficiency score (IES)
/
parallel processing
/
subitizing
/
Weber’s law
Cite this article
Download citation ▾
Wei Liu, Chunhui Wang, Jinglin Tian, Guido Marco Cicchini.
Subitizing endures in sequential rather than simultaneous comparison tasks.
Psych Journal, 2024, 13(5): 726-737 DOI:10.1002/pchj.750
| [1] |
Anobile, G., Arrighi, R., & Burr, D. C. (2019). Simultaneous and sequential subitizing are separate systems, and neither predicts math abilities. Journal of Experimental Child Psychology, 178, 86–103.
|
| [2] |
Anobile, G., Cicchini, G. M., & Burr, D. C. (2014). Separate mechanisms for perception of numerosity and density. Psychological Science, 25(1), 265–270.
|
| [3] |
Anobile, G., Cicchini, G. M., & Burr, D. C. (2016). Number as a primary perceptual attribute: A review. Perception, 45(1-2), 5–31.
|
| [4] |
Anobile, G., Stievano, P., & Burr, D. C. (2013). Visual sustained attention and numerosity sensitivity correlate with math achievement in children. Journal of Experimental Child Psychology, 116, 380–391.
|
| [5] |
Anobile, G., Tomaiuolo, F., Campana, S., & Cicchini, G. M. (2020). Three-systems for visual numerosity: A single case study. Neuropsychologia, 136, 107259.
|
| [6] |
Ashkenazi, S., Mark-Zigdon, N., & Henik, A. (2013). Do subitizing deficits in developmental dyscalculia involve pattern recognition weakness? Developmental Science, 16(1), 35–46.
|
| [7] |
Bugden, S., & Ansari, D. (2011). Individual differences in children’s mathematical competence are related to the intentional but not automatic processing of Arabic numerals. Cognition, 118(20111), 32–44.
|
| [8] |
Burr, D. C., Anobile, G., & Turi, M. (2011). Adaptation affects both high and low (subitized) numbers under conditions of high attentional load. Seeing and Perceiving, 24(2), 141–150.
|
| [9] |
Burr, D. C., Turi, M., & Anobile, G. (2010). Subitizing but not estimation of numerosity requires attentional resources. Journal of Vision, 10(6), 20.
|
| [10] |
Camos, V., & Tillmann, B. (2008). Discontinuity in the enumeration of sequentially presented auditory and visual stimuli. Cognition, 107(3), 1135–1143.
|
| [11] |
Cicchini, G. M., Anobile, G., & Burr, D. C. (2016). Spontaneous perception of numerosity in humans. Nature Communications, 7, 12536.
|
| [12] |
Cicchini, G. M., Anobile, G., & Burr, D. C. (2019). Spontaneous representation of numerosity in typical and dyscalculic development. Cortex, 114, 151–163.
|
| [13] |
Cicchini, G. M., Anobile, G., Chelli, E., Arrighi, R., & Burr, D. C. (2022). Uncertainty and prior assumptions, rather than innate logarithmic encoding, explain nonlinear number-to-space mapping. Psychological Science, 33(1), 121–134.
|
| [14] |
Dehaene, S. (2003). The neural basis of the weber–Fechner law: A logarithmic mental number line. TRENDS in Cognitive Sciences, 7(4), 145–147.
|
| [15] |
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007). G*power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavioral Research Methods, 39(2), 175–191.
|
| [16] |
Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: Evidence from Infants’ manual search. Developmental Science, 6(5), 568–584.
|
| [17] |
Gallistel, C. R., & Gelman, R. (2000). Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences, 4(2), 59–65.
|
| [18] |
Halberda, J., Sires, S. F., & Feigenson, L. (2006). Multiple spatially overlapping sets can Be enumerated in parallel. Psychological Science, 17(7), 572–576. http://www.jstor.org/stable/40064413
|
| [19] |
Hughes, M. M., Linck, J. A., Bowles, A. R., Koeth, J. T., & Bunting, M. F. (2014). Alternatives to switch-cost scoring in the task-switching paradigm: Their reliability and increased validity. Behavior Research Methods, 46(3), 702–721.
|
| [20] |
Jevons, W. (1871). The power of numerical discrimination. Nature, 3(67), 281–282.
|
| [21] |
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62(4), 498–525.
|
| [22] |
Kerzel, D. (2019). The precision of attentional selection is far worse than the precision of the underlying memory representation. Cognition, 186, 20–31.
|
| [23] |
Liu, W., Zheng, P., Huang, S., & Cicchini, G. M. (2020). Subitizing, unlike estimation, does not process sets in parallel. Scientific Reports, 10(1), 15689.
|
| [24] |
Liu, Y., Yin, J., & Liang, J. (2019). Why smoggy days suppress our mood: Automatic association between clarity and valence. Frontiers in Psychology, 10, 1580.
|
| [25] |
Melcher, D., Huber-Huber, C., & Wutz, A. (2021). Enumerating the forest before the trees: The time courses of estimation-based and individuation-based numerical processing. Attention, Perception, & Psychophysics, 83, 1215–1229.
|
| [26] |
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520.
|
| [27] |
Olivers, C. N. L., & Watson, D. G. (2008). Subitizing requires attention. Visual Cognition, 16(4), 439–462.
|
| [28] |
Palmer, J., Ames, C. T., & Lindsey, D. T. (1993). Measuring the effect of attention on simple visual search. Journal of Experimental Psychology: Human Perception and Performance, 19(1), 108–130.
|
| [29] |
Pomè A., Anobile, G., Cicchini, G. M., & Burr, D. C. (2019). Different reaction-times for subitizing, estimation, and texture. Journal of Vision, 19(6), 14.
|
| [30] |
Pomè A., Anobile, G., Cicchini, G. M., Scabia, A., & Burr, D. C. (2019). Higher attentional costs for numerosity estimation at high densities. Attention, Perception, & Psychophysics, 81, 2604–2611.
|
| [31] |
Ross, J. (2003). Visual discrimination of number without counting. Perception, 32(7), 867–870.
|
| [32] |
Schleifer, P., & Landerl, K. (2011). Subitizing and counting in typical and atypical development. Developmental Science, 14(2), 280–291.
|
| [33] |
Trick, L. M., & Pylyshyn, Z. W. (1993). What enumeration studies can show us about spatial attention: Evidence for limited capacity preattentive processing. Journal of Experimental Psychology: Human Perception and Performance, 19(2), 331–351.
|
| [34] |
Vandierendonck, A. (2017). A comparison of methods to combine speed and accuracy measures of performance: A rejoinder on the binning procedure. Behavior Research Methods, 49(2), 653–673.
|
| [35] |
Yousif, S. R., & Keil, F. C. (2020). Area, not number, dominates estimates of visual quantities. Scientific Reports, 10(1), 1–13.
|
RIGHTS & PERMISSIONS
2024 The Authors. PsyCh Journal published by Institute of Psychology, Chinese Academy of Sciences and John Wiley & Sons Australia, Ltd.