Bayesian modelling of the latent structure of individual differences in the numerical size-congruity effect

References

• Anders, R., Alario, F.-X., & Maanen, L. V. (2016). The shifted Wald distribution for response time data analysis. Psychological Methods, 21(3), 309–327. https://doi.org/10.1037/met0000066
   PubMed Web of Science ®Google Scholar
• Ashkenazi, S., Rubinsten, O., & Henik, A. (2009). Attention, automaticity, and developmental dyscalculia. Neuropsychology, 23(4), 535–540. https://doi.org/10.1037/a0015347
   PubMed Web of Science ®Google Scholar
• Bowman, K., & Faulkenberry, T. J. (2020). Modeling response times in the size-congruity effect: Early versus late interaction. PsyArXiV, https://doi.org/10.31234/osf.io/dns4t
   Google Scholar
• 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(1), 32–44. https://doi.org/10.1016/j.cognition.2010.09.005
   PubMed Web of Science ®Google Scholar
• Cohen Kadosh, R., Cohen Kadosh, K., Linden, D. E. J., Gevers, W., Berger, A., & & Henik, A. (2007). The brain locus of interaction between number and size: A combined functional magnetic resonance imaging and event-related potential study. Journal of Cognitive Neuroscience, 19(6), 957–970. https://doi.org/10.1162/jocn.2007.19.6.957
   PubMed Web of Science ®Google Scholar
• Davis-Stober, C. P., Dana, J., & Rouder, J. N. (2018). Estimation accuracy in the psychological sciences. PLOS ONE, 13(11), e0207239. https://doi.org/10.1371/journal.pone.0207239
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (1997). The number sense: How the mind creates mathematics. Oxford University Press.
   Google Scholar
• Faulkenberry, T. J. (2017). A single-boundary accumulator model of response times in an addition verification task. Frontiers in Psychology, 8, 1225 . https://doi.org/10.3389/fpsyg.2017.01225
   PubMed Web of Science ®Google Scholar
• Faulkenberry, T. J. (2019). A tutorial on generalizing the default Bayesian t-test via posterior sampling and encompassing priors. Communications for Statistical Applications and Methods, 26(2), 217–238. https://doi.org/10.29220/csam.2019.26.2.217
   Web of Science ®Google Scholar
• Faulkenberry, T. J. (2022). A note on the normality assumption for Bayesian models of constraint in behavioral individual differences. arXiv. https://arxiv.org/abs/2112.05503.
   Google Scholar
• Faulkenberry, T. J., Cruise, A., Lavro, D., & Shaki, S. (2016). Response trajectories capture the continuous dynamics of the size congruity effect. Acta Psychologica, 163, 114–123. https://doi.org/10.1016/j.actpsy.2015.11.010
   PubMed Web of Science ®Google Scholar
• Faulkenberry, T. J., Ly, A., & Wagenmakers, E.-J. (2020). Bayesian inference in numerical cognition: A tutorial using JASP. Journal of Numerical Cognition, 6(2), 231–259. https://doi.org/10.5964/jnc.v6i2.288
   Google Scholar
• Faulkenberry, T. J., Vick, A. D., & Bowman, K. A. (2018). A shifted Wald decomposition of the numerical size-congruity effect: Support for a late interaction account. Polish Psychological Bulletin, 49(4), 391–397. https://doi.org/10.24425/119507
   Google Scholar
• Fitousi, D. (2022). Conjoint measurement of physical size and numerical magnitude: Numerals do not automatically activate their semantic meaning. Psychonomic Bulletin & Review, 29(1), 134–144. https://doi.org/10.3758/s13423-021-01990-1
   PubMed Web of Science ®Google Scholar
• Fitousi, D., & Algom, D. (2006). Size congruity effects with two-digit numbers: Expanding the number line? Memory & Cognition, 34(2), 445–457. https://doi.org/10.3758/BF03193421
   PubMed Web of Science ®Google Scholar
• Fitousi, D., & Algom, D. (2018). A system factorial technology analysis of the size congruity effect: Implications for numerical cognition and stochastic modeling. Journal of Mathematical Psychology, 84, 57–73. https://doi.org/10.1016/j.jmp.2018.03.006
   Web of Science ®Google Scholar
• Girelli, L., Lucangeli, D., & Butterworth, B. (2000). The development of automaticity in accessing number magnitude. Journal of Experimental Child Psychology, 76(2), 104–122. https://doi.org/10.1006/jecp.2000.2564
   PubMed Web of Science ®Google Scholar
• Haaf, J. M., & Rouder, J. N. (2017). Developing constraint in Bayesian mixed models. Psychological Methods, 22(4), 779–798. https://doi.org/10.1037/met0000156
   PubMed Web of Science ®Google Scholar
• Haaf, J. M., & Rouder, J. N. (2018). Some do and some don’t? Accounting for variability of individual difference structures. Psychonomic Bulletin & Review, 26(3), 772–789. https://doi.org/10.3758/s13423-018-1522-x
   Web of Science ®Google Scholar
• Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10(4), 389–395. https://doi.org/10.3758/bf03202431
   PubMed Web of Science ®Google Scholar
• Jeffreys, H. (1961). The theory of probability (3rd ed.). Oxford University Press.
   Google Scholar
• Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773. https://doi.org/10.2307/2291091
   Web of Science ®Google Scholar
• Klugkist, I., Kato, B., & Hoijtink, H. (2005). Bayesian model selection using encompassing priors. Statistica Neerlandica, 59(1), 57–69. https://doi.org/10.1111/j.1467-9574.2005.00279.x
   Web of Science ®Google Scholar
• Krause, F., Bekkering, H., Pratt, J., & Lindemann, O. (2017). Interaction between numbers and size during visual search. Psychological Research, 81(3), 664–677. https://doi.org/10.1007/s00426-016-0771-4
   PubMed Web of Science ®Google Scholar
• Luce, R. D. (1986). Response times: Their role in inferring elementary mental organization. Oxford University Press.
   Google Scholar
• Mathôt, S., Schreij, D., & Theeuwes, J. (2011). Opensesame: An open-source, graphical experiment builder for the social sciences. Behavior Research Methods, 44(2), 314–324. https://doi.org/10.3758/s13428-011-0168-7
   Web of Science ®Google Scholar
• Morey, R. D., & Rouder, J. N. (2018). BayesFactor: Computation of Bayes factors for common designs. https://CRAN.R-project.org/package=BayesFactor
   Google Scholar
• Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520. https://doi.org/10.1038/2151519a0
   PubMed Web of Science ®Google Scholar
• Mussolin, C., Mejias, S., & Noël, M.-P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1), 10–25. https://doi.org/10.1016/j.cognition.2009.10.006
   PubMed Web of Science ®Google Scholar
• Paivio, A. (1975). Perceptual comparisons through the mind’s eye. Memory & Cognition, 3(6), 635–647. https://doi.org/10.3758/bf03198229
   PubMed Web of Science ®Google Scholar
• Pratte, M. S., Rouder, J. N., Morey, R. D., & Feng, C. (2010). Exploring the differences in distributional properties between stroop and simon effects using delta plots. Attention, Perception & Psychophysics, 72(7), 2013–2025. https://doi.org/10.3758/app.72.7.2013
   PubMed Web of Science ®Google Scholar
• R Core Team. (2020). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org
   Google Scholar
• Risko, E. F., Maloney, E. A., & Fugelsang, J. A. (2013). Paying attention to attention: evidence for an attentional contribution to the size congruity effect. Attention, Perception, & Psychophysics, 75(6), 1137–1147. http://dx.doi.org/10.3758/s13414-013-0477-2
   PubMed Web of Science ®Google Scholar
• Rouder, J. N., Morey, R. D., Speckman, P. L., & Province, J. M. (2012). Default Bayes factors for ANOVA designs. Journal of Mathematical Psychology, 56(5), 356–374. https://doi.org/10.1016/j.jmp.2012.08.001
   Web of Science ®Google Scholar
• Rouder, J. N., Province, J. M., Morey, R. D., Gomez, P., & Heathcote, A. (2014). The lognormal race: A cognitive-process model of choice and latency with desirable psychometric properties. Psychometrika, 80(2), 491–513. https://doi.org/10.1007/s11336-013-9396-3
   PubMed Web of Science ®Google Scholar
• Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16(2), 225–237. https://doi.org/10.3758/pbr.16.2.225
   PubMed Web of Science ®Google Scholar
• Rubinsten, O., Henik, A., Berger, A., & Shahar-Shalev, S. (2002). The development of internal representations of magnitude and their association with Arabic numerals. Journal of Experimental Child Psychology, 81(1), 74–92. https://doi.org/10.1006/jecp.2001.2645
   PubMed Web of Science ®Google Scholar
• Santens, S., & Verguts, T. (2011). The size congruity effect: Is bigger always more? Cognition, 118(1), 94–110. https://doi.org/10.1016/j.cognition.2010.10.014
   PubMed Web of Science ®Google Scholar
• Schwarz, W., & Heinze, H. J. (1998). On the interaction of numerical and size information in digit comparison: A behavioral and event-related potential study. Neuropsychologia, 36(11), 1167–1179. https://doi.org/10.1016/s0028-3932(98)00001-3
   PubMed Web of Science ®Google Scholar
• Sobel, K. V., Puri, A. M., & Faulkenberry, T. J. (2016). Bottom-up and top-down attentional contributions to the size congruity effect. Attention, Perception, & Psychophysics, 78(5), 1324–1336. https://doi.org/10.3758/s13414-016-1098-3
   PubMed Web of Science ®Google Scholar
• Sobel, K. V., Puri, A. M., Faulkenberry, T. J., & Dague, T. D. (2017). Visual search for conjunctions of physical and numerical size shows that they are processed independently. Journal of Experimental Psychology: Human Perception and Performance, 43(3), 444–453. https://doi.org/10.1037/xhp0000323
   PubMed Web of Science ®Google Scholar
• Szűcs, D., & Soltész, F. (2007). Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm. Neuropsychologia, 45(14), 3190–3202. https://doi.org/10.1016/j.neuropsychologia.2007.06.013
   PubMed Web of Science ®Google Scholar
• Szűcs, D., & Soltész, F. (2008). The interaction of task-relevant and task-irrelevant stimulus features in the number/size congruency paradigm: An ERP study. Brain Research, 1190, 143–158. https://doi.org/10.1016/j.brainres.2007.11.010
   PubMed Web of Science ®Google Scholar
• Vogel, S. E., Faulkenberry, T. J., & Grabner, R. H. (2021). Quantitative and qualitative differences in the canonical and the reverse distance effect and their selective association with arithmetic and mathematical competencies. Frontiers in Education, 6, 655747. https://doi.org/10.3389/feduc.2021.655747
   Google Scholar
• Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In P. K. Goel, & A. Zellner (Eds.), Bayesian inference and decision techniques: Essays in honor of Bruno de Finetti (pp. 233–243). Elsevier.
   Google Scholar