Individual differences influence two-digit number processing, but not their analog magnitude processing: a large-scale online study

  • Stefan Huber
  • Hans-Christoph Nuerk
  • Ulf-Dietrich Reips
  • Mojtaba Soltanlou
Original Article


Symbolic magnitude comparison is one of the most well-studied cognitive processes in research on numerical cognition. However, while the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to individual differences influencing symbolic magnitude comparison. Employing a two-digit number comparison task in an online setting, we replicated previous effects, including the distance effect, the unit-decade compatibility effect, and the effect of cognitive control on the adaptation to filler items, in a large-scale study in 452 adults. Additionally, we observed that the most influential individual differences were participants’ first language, time spent playing computer games and gender, followed by reported alcohol consumption, age and mathematical ability. Participants who used a first language with a left-to-right reading/writing direction were faster than those who read and wrote in the right-to-left direction. Reported playing time for computer games was correlated with faster reaction times. Female participants showed slower reaction times and a larger unit-decade compatibility effect than male participants. Participants who reported never consuming alcohol showed overall slower response times than others. Older participants were slower, but more accurate. Finally, higher grades in mathematics were associated with faster reaction times. We conclude that typical experiments on numerical cognition that employ a keyboard as an input device can also be run in an online setting. Moreover, while individual differences have no influence on domain-specific magnitude processing—apart from age, which increases the decade distance effect—they generally influence performance on a two-digit number comparison task.



We would like to thank all participants. We thank colleagues and friends, who translated the experiment into different languages and helped to access people. Hans-Christoph Nuerk and Mojtaba Soltanlou are supported by the Science Campus Tuebingen, project 8.4. Mojtaba Soltanlou is also supported by the DFG grant (NU 265/3-1) to Hans-Christoph Nuerk. Hans-Christoph Nuerk is further supported by the LEAD Graduate School & Research Network (GSC1028), a project of the Excellence Initiative of the German federal and state governments, and Stefan Huber is supported by the Leibniz-Competition Fund (SAW-2014-IWM-4) providing funding to Elise Klein. Finally, we thank Julianne Skinner for the language proofreading of the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. Anderson, J. R. (1982). Acquisition of cognitive skill. Psychological review, 89(4), 369.CrossRefGoogle Scholar
  2. Baayen, R. H., & Milin, P. (2010). Analyzing reaction times. International Journal of Psychological Research, 3(2), 12–28.CrossRefGoogle Scholar
  3. Bahnmueller, J., Huber, S., Nuerk, H.-C., Göbel, S. M., & Moeller, K. (2016). Processing multi-digit numbers: A translingual eye-tracking study. Psychological Research Psychologische Forschung, 80(3), 422–433. Scholar
  4. Bahnmueller, J., Moeller, K., Mann, A., & Nuerk, H.-C. (2015). On the limits of language influences on numerical cognition – no inversion effects in three-digit number magnitude processing in adults. Frontiers in Psychology, 6, 1216. Scholar
  5. Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255–278. Scholar
  6. Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. Scholar
  7. Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological), 57(1), 289–300. Scholar
  8. Birnbaum, M. H. (2004). Human research and data collection via the internet. Annual Review of Psychology, 55(1), 803–832. Scholar
  9. Botvinick, M. M., Braver, T. S., Barch, D. M., Carter, C. S., & Cohen, J. D. (2001). Conflict monitoring and cognitive control. Psychological review, 108(3), 624. Scholar
  10. Bull, R., Cleland, A. A., & Mitchell, T. (2013). Sex differences in the spatial representation of number. Journal of Experimental Psychology: General, 142(1), 181–192. Scholar
  11. Bull, R., & Lee, K. (2014). Executive functioning and mathematics achievement. Child Development Perspectives, 8(1), 36–41. Scholar
  12. Cahill, L. (2006). Why sex matters for neuroscience. Nature Reviews Neuroscience, 7(6), 477–484. Scholar
  13. Cappelletti, M., Didino, D., Stoianov, I., & Zorzi, M. (2014). Number skills are maintained in healthy ageing. Cognitive Psychology, 69, 25–45. Scholar
  14. Castronovo, J., & Göbel, S. M. (2012). Impact of high mathematics education on the number sense. PLoS One, 7(4), e33832. Scholar
  15. Cipora, K., Patro, K., & Nuerk, H.-C. (2016). Situated influences on spatial-numerical associations. In T. Hubbard (Ed.), Spatial Biases in Perception and Cognition. Cambridge: Cambridge University Press.Google Scholar
  16. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. New York: Routledge Academic.Google Scholar
  17. Colzato, L. S., Hertsig, G., van den Wildenberg, W. P. M., & Hommel, B. (2010). Estrogen modulates inhibitory control in healthy human females: Evidence from the stop-signal paradigm. Neuroscience, 167(3), 709–715. Scholar
  18. Crump, M. J. C., McDonnell, J. V., & Gureckis, T. M. (2013). Evaluating amazon’s mechanical turk as a tool for experimental behavioral research. PLoS One, 8(3), e57410. Scholar
  19. De Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48–55. Scholar
  20. Deary, I. J., & Der, G. (2005). Reaction time, age, and cognitive ability: Longitudinal findings from age 16 to 63 years in representative population samples. Aging, Neuropsychology, and Cognition, 12(2), 187–215. Scholar
  21. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371–396. Scholar
  22. Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16(3), 626–641.PubMedGoogle Scholar
  23. Der, G., & Deary, I. J. (2006). Age and sex differences in reaction time in adulthood: Results from the United Kingdom Health and Lifestyle Survey. Psychology and Aging, 21(1), 62–73. Scholar
  24. Dietrich, J. F., Huber, S., Moeller, K., & Klein, E. (2015). The influence of math anxiety on symbolic and non-symbolic magnitude processing. Frontiers in Psychology, 6:1621. Scholar
  25. Dietrich, J. F., Huber, S., & Nuerk, H.-C. (2015). Methodological aspects to be considered when measuring the approximate number system (ANS) – a research review. Frontiers in Psychology, 6:295. Scholar
  26. Dye, M. W. G., Green, C. S., & Bavelier, D. (2009a). Increasing speed of processing with action video games. Current Directions in Psychological Science, 18(6), 321–326. Scholar
  27. Dye, M. W. G., Green, C. S., & Bavelier, D. (2009b). The development of attention skills in action video game players. Neuropsychologia, 47(8–9), 1780–1789. Scholar
  28. Dykiert, D., Der, G., Starr, J. M., & Deary, I. J. (2012). Sex differences in reaction time mean and intraindividual variability across the life span. Developmental Psychology, 48(5), 1262–1276. Scholar
  29. Easdon, C., Izenberg, A., Armilio, M. L., Yu, H., & Alain, C. (2005). Alcohol consumption impairs stimulus- and error-related processing during a Go/No-Go task. Cognitive Brain Research, 25(3), 873–883. Scholar
  30. Fabbri, M. (2013). Finger counting habits and spatial-numerical association in horizontal and vertical orientations. Journal of Cognition & Culture, 13(1/2), 95–110. Scholar
  31. Fischer, M. H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44(4), 386–392. Scholar
  32. Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition—from single digits to arithmetic. The Quarterly Journal of Experimental Psychology, 67(8), 1461–1483. Scholar
  33. Ganor-Stern, D., & Tzelgov, J. (2008). Across-notation automatic numerical processing. Journal of Experimental Psychology: Learning, Memory, and Cognition, 34(2), 430–437. Scholar
  34. Ganor-Stern, D., & Tzelgov, J. (2010). Across-notation automatic processing of two-digit numbers. Experimental Psychology, 58(2), 147–153. Scholar
  35. Hatta, T., & Nagaya, K. (2009). Menstrual cycle phase effects on memory and Stroop task performance. Archives of Sexual Behavior, 38(5), 821–827. Scholar
  36. Hinrichs, J. V., Berie, J. L., & Mosell, M. K. (1982). Place information in multidigit number comparison. Memory & Cognition, 10(5), 487–495. Scholar
  37. Hinrichs, J. V., Yurko, D. S., & Hu, J.-M. (1981). Two-digit number comparison: Use of place information. Journal of Experimental Psychology: Human Perception and Performance, 7(4), 890–901.Google Scholar
  38. Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology. Scholar
  39. Huber, S., Klein, E., Graf, M., Nuerk, H.-C., Moeller, K., & Willmes, K. (2015). Embodied markedness of parity? Examining handedness effects on parity judgments. Psychological Research, 79(6), 963–977. Scholar
  40. Huber, S., Mann, A., Nuerk, H. C., & Moeller, K. (2014). Cognitive control in number magnitude processing: evidence from eye-tracking. Psychological Research Psychologische Forschung, 78(4), 539–548. Scholar
  41. Huber, S., Moeller, K., Nuerk, H.-C., & Willmes, K. (2013). A computational modeling approach on three-digit number processing. Topics in Cognitive Science, 5(2), 317–334. Scholar
  42. Huber, S., Nuerk, H.-C., Willmes, K., & Moeller, K. (2016). A general model framework for multisymbol number comparison. Psychological Review, 123(6), 667–695. Scholar
  43. Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59(4), 434–446. Scholar
  44. Kallai, A. Y., & Tzelgov, J. (2012). The place-value of a digit in multi-digit numbers is processed automatically. Journal of Experimental Psychology. Learning, Memory, and Cognition, 38(5), 1221–133.CrossRefPubMedGoogle Scholar
  45. Killgore, W. D. S. (2010). Effects of sleep deprivation on cognition. In G. A. Kerkhof & H. P. A. Van Dongen (Eds.), Progress in Brain Research—Human Sleep and Cognition (Vol. 185, pp. 105–129). Amsterdam: Elsevier. Scholar
  46. Krantz, J. H., & Reips, U.-D. (2017). The state of web-based research: A survey and call for inclusion in curricula. Behavior Research Methods, 49(5), 1621–1629.CrossRefPubMedGoogle Scholar
  47. Kuznetsova, A., Brockhoff, P. B., & Christensen, R. H. (2016). lmerTest: Tests in linear mixed effects models.Google Scholar
  48. Leys, C., Ley, C., Klein, O., Bernard, P., & Licata, L. (2013). Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median. Journal of Experimental Social Psychology, 49(4), 764–766. Scholar
  49. Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition. Scholar
  50. Macizo, P. (2017). Conflict resolution in two-digit number processing: evidence of an inhibitory mechanism. Psychological research, 81(1), 219–230. Scholar
  51. Macizo, P., & Herrera, A. (2011). Cognitive control in number processing: Evidence from the unit-decade compatibility effect. Acta Psychologica, 136(1), 112–118. Scholar
  52. Macizo, P., & Herrera, A. (2013). The processing of Arabic numbers is under cognitive control. Psychological Research Psychologische Forschung, 77(5), 651–658. Scholar
  53. Macizo, P., Herrera, A., Paolieri, D., & Román, P. (2010). Is there cross-language modulation when bilinguals process number words? Applied Psycholinguistics, 31(4), 651–669. Scholar
  54. Macizo, P., Herrera, A., Román, P., & Martín, M. C. (2011). The processing of two-digit numbers in bilinguals. British Journal of Psychology, 102(3), 464–477. Scholar
  55. Maloney, E. A., Risko, E. F., Preston, F., Ansari, D., & Fugelsang, J. (2010). Challenging the reliability and validity of cognitive measures: The case of the numerical distance effect. Acta Psychologica, 134(2), 154–161. Scholar
  56. Moeller, K., Klein, E., & Nuerk, H. (2013). Influences of cognitive control on numerical cognition—Adaptation by binding for implicit learning. Topics in Cognitive Science, 5, 335–353.CrossRefPubMedGoogle Scholar
  57. Moeller, K., Pixner, S., Zuber, J., Kaufmann, L., & Nuerk, H. C. (2011). Early place-value understanding as a precursor for later arithmetic performance - A longitudinal study on numerical development. Research in Developmental Disabilities, 32(5), 1837–1851. Scholar
  58. Moeller, K., Shaki, S., Göbel, S. M., & Nuerk, H.-C. (2015). Language influences number processing – A quadrilingual study. Cognition, 136(0), 150–155. Scholar
  59. Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520. Scholar
  60. Norris, J. E., McGeown, W. J., Guerrini, C., & Castronovo, J. (2015). Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing. Frontiers in Psychology, 6, 999. Scholar
  61. Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line: A review of multi-digit number processing. Zeitschrift Für Psychologie/Journal of Psychology, 219(1), 3–22.CrossRefGoogle Scholar
  62. Nuerk, H.-C., Moeller, K., & Willmes, K. (2015). Multi-digit number processing - Overview, conceptual clarifications, and language influences. In R. C. Kadosh & A. Dowker (Eds.), The Oxford Handbook of Numerical Cognition (pp. 106–139). Oxford: Oxford University Press.Google Scholar
  63. Nuerk, H.-C., Weger, U., & Willmes, K. (2001). Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition, 82(1), B25–B33. Scholar
  64. Nuerk, H.-C., Weger, U., & Willmes, K. (2005). Language effects in magnitude comparison: Small, but not irrelevant. Brain and Language, 92(3), 262–277. Scholar
  65. Nys, J., Ventura, P., Fernandes, T., Querido, L., Leybaert, J., & Content, A. (2013). Does math education modify the approximate number system? A comparison of schooled and unschooled adults. Trends in Neuroscience and Education, 2(1), 13–22. Scholar
  66. Patro, K., Nuerk, H.-C., & Cress, U. (2015). Does your body count? Embodied influences on the preferred counting direction of preschoolers. Journal of Cognitive Psychology, 27(4), 413–425. Scholar
  67. Pixner, S., Moeller, K., Hermanova, V., Nuerk, H. C., & Kaufmann, L. (2011). Whorf reloaded: Language effects on nonverbal number processing in first grade—A trilingual study. Journal of Experimental Child Psychology, 108(2), 371–382. Scholar
  68. Pletzer, B., Kronbichler, M., Nuerk, H.-C., & Kerschbaum, H. (2014). Hormonal contraceptives masculinize brain activation patterns in the absence of behavioral changes in two numerical tasks. Brain Research, 1543, 128–142. Scholar
  69. Prior, A., Katz, M., Mahajna, I., & Rubinsten, O. (2015). Number word structure in first and second language influences arithmetic skills. Frontiers in Psychology, 6, 266. Scholar
  70. Ratcliff, R. (1993). Methods for dealing with reaction time outliers. Psychological Bulletin, 114(3), 510–532. Scholar
  71. Ratinckx, E., Nuerk, H.-C., van Dijck, J. P., & Willmes, K. (2006). Effects of interhemispheric communication on two-digit arabic number processing. Cortex, 42(8), 1128–1137. Scholar
  72. Reips, U.-D. (2002). Standards for Internet-based experimenting. Experimental Psychology, 49(4), 243–256. Scholar
  73. Reips, U.-D. (2007). The methodology of Internet-based experiments. In A. Joinson, K. McKenna, T. Postmes & U.-D. Reips (Eds.), The Oxford Handbook of Internet Psychology (pp. 373–390). Oxford: Oxford University Press.Google Scholar
  74. Reips, U.-D. (2012). The methodology of Internet-based experiments. In A. N. Joinson, K. Y. A. McKenna, T. Postmes & U.-D. Reips (Eds.), Oxford Handbook of Internet Psychology (pp. 373–390). Oxford: Oxford University Press.Google Scholar
  75. Reips, U.-D., & Lengler, R. (2005). The Web Experiment List: A Web service for the recruitment of participants and archiving of Internet-based experiments. Behavior Research Methods, 37, 287–292.CrossRefPubMedGoogle Scholar
  76. Reips, U.-D., & Neuhaus, C. (2002). WEXTOR: A Web-based tool for generating and visualizing experimental designs and procedures. Behavior Research Methods, 34(2), 234–240.CrossRefGoogle Scholar
  77. Reuter-Lorenz, P. A., & Park, D. C. (2010). Human neuroscience and the aging mind: A new look at old problems. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences. Scholar
  78. Roberts, G. M. P., Newell, F., Simões-Franklin, C., & Garavan, H. (2008). Menstrual cycle phase modulates cognitive control over male but not female stimuli. Brain Research, 1224, 79–87. Scholar
  79. Salthouse, T. A. (1996). The processing-speed theory of adult age differences in cognition. Psychological Review, 103(3), 403–428. Scholar
  80. Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2016). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis. Developmental Science. Scholar
  81. Singmann, H., Bolker, B., Westfall, J., & Aust, F. (2016). afex: Analysis of Factorial Experiments.Google Scholar
  82. Steinborn, M. B., Bratzke, D., Rolke, B., Gordijn, M. C. M., Beersma, D. G. M., & Ulrich, R. (2010). The effect of 40 h of constant wakefulness on number comparison performance. Chronobiology International: The Journal of Biological & Medical Rhythm Research, 27(4), 807–825.CrossRefGoogle Scholar
  83. Stroop, J. R. (1935). Studies of interference in serial verbal reactions. Journal of Experimental Psychology, 18(6), 643–662.CrossRefGoogle Scholar
  84. Thomas, M., & Morwitz, V. (2005). Penny wise and pound foolish: The left-digit effect in price cognition. Journal of Consumer Research, 32(1), 54–64.CrossRefGoogle Scholar
  85. Van Opstal, F., & Verguts, T. (2011). The origins of the numerical distance effect: The same–different task. Journal of Cognitive Psychology, 23(1), 112–120.CrossRefGoogle Scholar
  86. Van Rinsveld, A., & Schiltz, C. (2016). Sixty-twelve = Seventy-two? A cross-linguistic comparison of children’s number transcoding. British Journal of Developmental Psychology, 34(3), 461–468. Scholar
  87. Van Rinsveld, A., Schiltz, C., Landerl, K., Brunner, M., & Ugen, S. (2016). Speaking two languages with different number naming systems: What implications for magnitude judgments in bilinguals at different stages of language acquisition? Cognitive Processing, 17(3), 225–241. Scholar
  88. Verguts, T., Fias, W., & Stevens, M. (2005). A model of exact small-number representation. Psychonomic Bulletin & Review, 12(1), 66–80. Scholar
  89. Verguts, T., & Notebaert, W. (2009). Adaptation by binding: a learning account of cognitive control. Trends in cognitive sciences, 13(6), 252–257.CrossRefPubMedGoogle Scholar
  90. Whelan, R. (2010). Effective analysis of reaction time data. The Psychological Record, 58(3), 475–482.CrossRefGoogle Scholar
  91. Wickham, H. (2009). ggplot2: Elegant graphics for data analysis. Springer-Verlag, New York.CrossRefGoogle Scholar
  92. Wilke, C. O. (2016). cowplot: Streamlined plot theme and plot annotations for ggplot2.Google Scholar
  93. Wood, G., Nuerk, H. C., Freitas, P., Freitas, G., & Willmes, K. (2006). What do semi-illiterate adults know about 2-digit arabic numbers? Cortex, 42(1), 48–56. Scholar
  94. Zebian, S., & Ansari, D. (2012). Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing. Psychonomic Bulletin & Review, 19(1), 93–100. Scholar

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Authors and Affiliations

  1. 1.Leibniz-Institut für WissensmedienTuebingenGermany
  2. 2.Department of PsychologyUniversity of TuebingenTuebingenGermany
  3. 3.LEAD Graduate School & Research NetworkUniversity of TuebingenTuebingenGermany
  4. 4.Department of PsychologyUniversity of KonstanzKonstanzGermany

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