Exploring the Variability in Reaction Times of Preschoolers at Risk of Attention-Deficit/Hyperactivity Disorder: an ex-Gaussian Analysis

  • Shoou-Lian Hwang-Gu
  • Yu-Chi Chen
  • Sophie Hsin-Yi Liang
  • Hsing-Chang Ni
  • Hsiang-Yuan Lin
  • Chiao-Fan Lin
  • Susan Shur-Fen GauEmail author


Reaction times (RTs) are typically slower and more variable in individuals with attention-deficit/hyperactivity disorder (ADHD). Analysis of the ex-Gaussian RT distribution, which is described by mu, sigma (mean and standard deviation, respectively, of the normal distribution) and tau (that of exponential distribution), reveals that individuals with ADHD do not display overall slower RTs but have a high proportion of extremely slow RTs, represented by a high tau value. Although this is a vital component for describing ADHD-related RT variability in school-aged children, adolescents, and adults, it has not been thoroughly studied at the preschool age. We assessed 65 preschoolers at risk of ADHD and 98 typically developing preschoolers with the Conners’ Kiddie Continuous Performance Test (K-CPT) and parental and teacher reports of ADHD symptoms. We found that preschoolers at risk of ADHD had greater values for RT standard deviation, sigma, and tau than typically developing preschoolers at long inter-stimulus intervals (ISIs) (3 s), but not at short ISIs (1.5 s). This suggests that attention problems in preschool children may only be apparent in the tasks with a relatively slow event rate. Our study demonstrates that the ex-Gaussian tau value is essential for describing the inattentive component of task performance in preschoolers with heightened ADHD symptoms. Furthermore, the fact that the tau effect was modulated by ISI suggests that the longer duration (3 s vs. 1.5 s) is a non-optimal energetic state in preschoolers at risk of ADHD, and that this might account for the subtle attentional flaw in task performance.


ADHD Reaction time Preschool children Ex-Gaussian 



This study was supported by grants from the Ministry of Science and Technology (MOST 103-2410-H-182-003-MY3), and Chang Gung University (NMRPD1D0131, NMRPD1D0132, NMRPD1D0133), Taiwan. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors would like to express our thanks to all the participants and their parents and our research assistants for their contribution to this study.

Compliance with Ethical Standards

Conflict of Interest

The authors have declared that they have no competing conflicts of interest.

Ethical Approval

All procedures involving human participants were in accordance with the ethical standards of the institutional and national research committees, the 1964 Helsinki Declaration, and its later amendments, or comparable ethical standards.

Informed Consent

This study was approved by the Research Ethics Committee of the National Taiwan University Hospital and by the Chang Gung Medical Foundation Institutional Review Board, and parents’ written informed consent and child assent were obtained before study implementation.

Supplementary material

10802_2018_508_MOESM1_ESM.docx (16 kb)
ESM 1 (DOCX 16 kb)


  1. Achenbach, T. M., & Ruffle, T. M. (2000). The child behavior checklist and related forms for assessing behavioral/emotional problems and competencies. Pediatrics in Review, 21(8), 265–271. Scholar
  2. American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders, 5th edition (DSM-5). In DS. Washington: American Psychiatric Press.Google Scholar
  3. Barnard, H., Rao, R., Xu, Y., Froehlich, T., Epstein, J., Lanphear, B. P., & Yolton, K. (2015). Association of the Conners' kiddie continuous performance test (K-CPT) performance and parent-report measures of behavior and executive functioning. Journal of Attention Disorders, 22(11), 1056–1065. Scholar
  4. Chen, Y. C., Hwang-Gu, S. L., Ni, H. C., Liang, S. H. Y., Lin, H. Y., Lin, C. F., Tseng, Y. H., & Gau, S. S. F. (2017). Relationship between parenting stress and informant discrepancies on symptoms of ADHD/ODD and internalizing behaviors in preschool children. PLoS One, 12, e0183467. Scholar
  5. Chiang, H. L., & Gau, S. S. (2016). Comorbid psychiatric conditions as mediators to predict later social adjustment in youths with autism spectrum disorder. Journal of Child Psychology and Psychiatry, 57, 103–111. Scholar
  6. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates.Google Scholar
  7. Conners, C. (2006). Conners’ Kiddie Continuous Performance TEST North Tonawanda, NY: Multi-Health Systems.Google Scholar
  8. De Nijs, P. F., Ferdinand, R. F., de Bruin, E. I., Dekker, M. C., van Duijn, C. M., & Verhulst, D. C. (2004). Attention-deficit/hyperactivity disorder (ADHD): Parents’ judgment about school, teachers’ judgment about home. European Child & Adolescent Psychiatry, 13(5), 315–320. Scholar
  9. Egger, H. L., Kondo, D., & Angold, A. (2006). The epidemiology and diagnostic issues in preschool attention-deficit/ hyperactivity disorder – A review. Infants and Young Children, 19, 109–122.CrossRefGoogle Scholar
  10. Epstein, J. N., Langberg, J. M., Rosen, P. J., Graham, A., Narad, M. E., Antonini, T. N., Brinkman, W. B., Froehlich, T., Simon, J. O., & Altaye, M. (2011). Evidence for higher reaction time variability for children with ADHD on a range of cognitive tasks including reward and event rate manipulations. Neuropsychology, 25(4), 427–441.CrossRefGoogle Scholar
  11. Ezpeleta, L., & Granero, R. (2015). Executive functions in preschoolers with ADHD, ODD, and comorbid ADHD-ODD: Evidence from ecological and performance-based measures. Journal of Neuropsychology, 9(2), 258–270. Scholar
  12. Gau, S. F., & Soong, W. T. (1999). Psychiatric comorbidity of adolescents with sleep terrors or sleepwalking: A case-control study. The Australian and New Zealand Journal of Psychiatry, 33(5), 734–739.CrossRefGoogle Scholar
  13. Gau, S. S. F., Chong, M. Y., Chen, T. H., & Cheng, A. T. (2005). A 3-year panel study of mental disorders among adolescents in Taiwan. American Journal of Psychiatry, 162(7), 1344–1350. Scholar
  14. Gau, S. S. F., Shang, C. Y., Liu, S. K., Lin, C. H., Swanson, J. M., Liu, Y. C., & Tu, C. L. (2008). Psychometric properties of the Chinese version of the Swanson, Nolan, and Pelham, version IV scale – Parent form. International Journal of Methods in Psychiatric Research, 17(1), 35–44. Scholar
  15. Gau, S. S. F., Lin, C. H., Hu, F. C., Shang, C. Y., Swanson, J. M., Liu, Y. C., & Liu, S. K. (2009). Psychometric properties of the Chinese version of the Swanson, Nolan, and Pelham, version IV scale – Teacher form. Journal of Pediatric Psychology, 34(8), 850–861. Scholar
  16. Geurts, H. M., Grasman, R. P., Verte, S., Oosterlaan, J., Roeyers, H., van Kammen, S. M., & Sergeant, J. A. (2008). Intra-individual variability in ADHD, autism spectrum disorders and Tourette's syndrome. Neuropsychologia, 46(13), 3030–3041. Scholar
  17. Gmehlin, D., Fuermaier, A. B., Walther, S., Tucha, L., Koerts, J., Lange, K. W., et al. (2016). Attentional lapses of adults with attention deficit hyperactivity disorder in tasks of sustained attention. Archives of Clinical Neuropsychology, 31(4), 343–357. Scholar
  18. Gu, S. L. H., Gau, S. S. F., Tzang, S. W., & Hsu, W. Y. (2013). The ex-Gaussian distribution of reaction times in adolescents with attention-deficit/hyperactivity disorder. Research in Developmental Disabilities, 34(11), 3709–3719. Scholar
  19. Halperin, J. M., & Schulz, K. P. (2006). Revisiting the role of the prefrontal cortex in the pathophysiology of attention-deficit/hyperactivity disorder. Psychological Bulletin, 132(4), 560–581. Scholar
  20. Hasson, R., & Fine, J. G. (2012). Gender differences among children with ADHD on continuous performance tests: A meta-analytic review. Journal of Attention Disorders, 16(3), 190–198.CrossRefGoogle Scholar
  21. Heathcote, A., Popiel, S. J., & Mewhort, D. J. (1991). Analysis of response time distributions: An example using the Stroop task. Psychological Bulletin, 109(2), 340–347.CrossRefGoogle Scholar
  22. Henriquez-Henriquez, M. P., Billeke, P., Henriquez, H., Zamorano, F. J., Rothhammer, F., & Aboitiz, F. (2014). Intra-individual response variability assessed by ex-Gaussian analysis may be a new endophenotype for attention-deficit/hyperactivity disorder. Frontiers in Psychiatry, 5.
  23. Hervey, A. S., Epstein, J. N., Curry, J. F., Tonev, S., Eugene Arnold, L., Keith Conners, C., Hinshaw, S. P., Swanson, J. M., & Hechtman, L. (2006). Reaction time distribution analysis of neuropsychological performance in an ADHD sample. Child Neuropsychology, 12(2), 125–140. Scholar
  24. Ho, T. P., Luk, E. S. L., Leung, P. W. L., Taylor, E., Lieh-Mak, F., & Bacon-Shone, J. (1996). Situational versus pervasive hyperactivity in a community sample. Psychological Medicine, 26(2), 309–321. Scholar
  25. Jensen, P. S., Kettle, L., Roper, M. T., Sloan, M. T., Dulcan, M. K., Hoven, C., et al. (1999). Are stimulants overprescribed? Treatment of ADHD in four U.S. communities. Journal of the American Academy of Child and Adolescent Psychiatry, 38(7), 797–804. Scholar
  26. Kanaka, N., Matsuda, T., Tomimoto, Y., Noda, Y., Matsushima, E., Matsuura, M., & Kojima, T. (2008). Measurement of development of cognitive and attention functions in children using continuous performance test. Psychiatry of Clinical Neuroscise, 62(2), 135–141. Scholar
  27. Karalunas, S. L., Geurts, H. M., Konrad, K., Bender, S., & Nigg, J. T. (2014). Annual research review: Reaction time variability in ADHD and autism spectrum disorders: Measurement and mechanisms of a proposed trans-diagnostic phenotype. Journal of Child Psychology and Psychiatry, 55(6), 685–710. Scholar
  28. Kofler, M. J., Rapport, M. D., Sarver, D. E., Raiker, J. S., Orban, S. A., Friedman, L. M., & Kolomeyer, E. G. (2013). Reaction time variability in ADHD: A meta-analytic review of 319 studies. Clinical Psychology Review, 33(6), 795–811. Scholar
  29. Lacouture, Y., & Cousineau, D. (2008). How to use MATLAB to fit the ex-Gaussian and other probability function to a distribution of response times. Tutorial in Quantitative Methods for Psychology, 4, 35–45.CrossRefGoogle Scholar
  30. Lahey, B. B., Pelham, W. E., Loney, J., Kipp, H., Ehrhardt, A. M. E., Lee, S., . . . Massetti, G. (2004). Three-year predictive validity of DSM-IV attention deficit hyperactivity disorder in children diagnosed at 4–6 years of age. American Journal of Psychiatry, 161, 2014–2020. Scholar
  31. Lahey, B. B., Pelham, W. E., Loney, J., Lee, S. S., & Willcutt, E. (2005). Instability of the DSM-IV subtypes of ADHD: From preschool through elementary school. Archives of General Psychiatry, 62(8), 896–902. Scholar
  32. Leth-Steensen, C., Elbaz, Z. K., & Douglas, V. I. (2000). Mean response times, variability, and skew in the responding of ADHD children: A response time distributional approach. Acta Psychologica, 104(2), 167–190. Scholar
  33. Lin, H. Y., Gau, S. S. F., Huang-Gu, S. L., Shang, C. Y., Wu, Y. H., & Tseng, W. Y. (2014). Neural substrates of behavioral variability in attention deficit hyperactivity disorder: Based on ex-Gaussian reaction time distribution and diffusion spectrum imaging tractography. Psychological Medicine, 44(8), 1751–1764. Scholar
  34. Lin, H. Y., Hwang-Gu, S. L., & Gau, S. S. F. (2015). Intra-individual reaction time variability based on ex-Gaussian distribution as a potential endophenotype for attention-deficit/hyperactivity disorder. Acta Psychiatrica Scandinavica, 132(1), 39–50. Scholar
  35. Luce, R. D. (1986). Response times: Their role in inferring elementary mental organization. New York: Oxford University Press.Google Scholar
  36. Mahone, E. M., Pillion, J. P., Hoffman, J., Hiemenz, J. R., & Denckla, M. B. (2005). Construct validity of the auditory continuous performance test for preschoolers. Developmental Neuropsychology, 27(1), 11–33. Scholar
  37. Mahone, E. M., Mostofsky, S. H., Lasker, A. G., Zee, D., & Denckla, M. B. (2009). Oculomotor anomalies in attention-deficit/hyperactivity disorder: Evidence for deficits in response preparation and inhibition. Journal of the American Academy of Child and Adolescent Psychiatry, 48(7), 749–756. Scholar
  38. Mannuzza, S., Klein, R. G., & MoultonIII, J. L. (2002). Young adult outcome of children with “situational” hyperactivity: A prospective, controlled follow-up study. Journal of Abnormal Child Psychology, 30(2), 191–198. Scholar
  39. McArdle, P. (2004). Attention-deficit hyperactivity disorder and life-span development. British Journal of Psychiatry, 184, 468–469. Scholar
  40. Metin, B., Roeyers, H., Wiersema, J. R., van der Meere, J., & Sonuga-Barke, E. (2012). A meta-analytic study of event rate effects on go/no-go performance in attention-deficit/hyperactivity disorder. Biological Psychiatry, 72(12), 990–996. Scholar
  41. Metin, B., Wiersema, J. R., Verguts, T., Gasthuys, R., van Der Meere, J. J., Roeyers, H., & Sonuga-Barke, E. (2014). Event rate and reaction time performance in ADHD: Testing predictions from the state regulation deficit hypothesis using an ex-Gaussian model. Child Neuropsycholgy, 22(1), 99–109. Scholar
  42. Metin, B., Krebs, R. M., Wiersema, J. R., Verguts, T., Gasthuys, R., van der Meere, J. J., Achten, E., Roeyers, H., & Sonuga-Barke, E. (2015). Dysfunctional modulation of default mode network activity in attentiondeficit/ hyperactivitydisorder. Journal of Abnormal Psychology, 124(1), 208–214.
  43. Mitsis, E. M., McKAY, K. E., Schulz, K. P., Newcorn, J. H., & Halperin, J. M. (2000). Parent–teacher concordance for DSM-IV attention-deficit/hyperactivity disorder in a clinic-referred sample. Journal of the American Academy of Child & Adolescent Psychiatry, 39(3), 308–313. Scholar
  44. Park, M. H., Kweon, Y. S., Lee, S. J., Park, E. J., Lee, C., & Lee, C. U. (2011). Differences in performance of ADHD children on a visual and auditory continuous performance test according to IQ. Psychiatry Investigation, 8(3), 227–233. Scholar
  45. Pauli-Pott, U., & Becker, K. (2011). Neuropsychological basic deficits in preschoolers at risk for ADHD: A meta-analysis. Clinical Psychology Review, 31(4), 626–637. Scholar
  46. Pires Tde, O., da Silva, C. M., & de Assis, S. G. (2013). Association between family environment and attention deficit hyperactivity disorder in children--mothers' and teachers' views. BMC Psychiatry, 13(215).
  47. Schoemaker, K., Mulder, H., Dekovic, M., & Matthys, W. (2013). Executive functions in preschool children with externalizing behavior problems: A meta-analysis. Journal of Abnormal Child Psychology, 41(3), 457–471. Scholar
  48. Shang, C. Y., Wu, Y. H., Gau, S. S., & Tseng, W. Y. (2013). Disturbed microstructural integrity of the frontostriatal fiber pathways and executive dysfunction in children with attention deficit hyperactivity disorder. Psychological Medicine, 43, 1093–1107. Scholar
  49. Sjöwall, D., Backman, A., & Thorell, L. B. (2015). Neuropsychological heterogeneity in preschool ADHD: Investigating the interplay between cognitive, affective and motivation-based forms of regulation. Journal of Abnormal Child Psychology, 43(4), 669–680. Scholar
  50. Sonuga-Barke, E. J. S. (1994). Annotation: On dysfunction and function in psychological theories of childhood disorder. Journal of Child Psychology and Psychiatry, 35, 801–815. Scholar
  51. Sonuga-Barke, E. J., & Halperin, J. M. (2010). Developmental phenotypes and causal pathways in attention deficit/hyperactivity disorder: Potential targets for early intervention? Journal of Child Psychology and Psychiatry, 51(4), 368–389. Scholar
  52. Sonuga-Barke, E. J. S., Taylor, E., Sembi, S., & Smith, J. (1992). Hyperactivity and delay aversion I: The effect of delay on choice. Journal of Child Psychology and Psychiatry, 33, 387–398. Scholar
  53. Swanson, J. M., Kraemer, H. C., Hinshaw, S. P., Arnold, L. E., Conners, C. K., Abikoff, H. B., et al. (2001). Clinical relevance of the primary findings of the MTA: Success rates based on severity of ADHD and ODD symptoms at the end of treatment. Journal of the American Academy of Child & Adolescent Psychiatry, 40(2), 168–179. Scholar
  54. Tarantino, V., Cutini, S., Mogentale, C., & Bisiacchi, P. S. (2013). Time-on-task in children with ADHD: An ex-Gaussian analysis. Journal of the International Neuropsychological Society, 19(7), 820–828. Scholar
  55. Thorell, L. B. (2007). Do delay aversion and executive function deficits make distinct contributions to the functional impact of ADHD symptoms? A study of early academic skill deficits. Journal of Child Psychology and Psychiatry, 48(11), 1061–1070. Scholar
  56. Ulrich, R., & Miller, J. (1994). Effects of truncation on reaction time analysis. Journal of Experimental Psychology: General, 123(1), 34–80. Scholar
  57. Van Der Meere, J., Borger, N., & Wiersema, J. R. (2010). ADHD: State regulation and motivation. CML – Psychiatry, 21, 14–20.Google Scholar
  58. Wåhlstedt, C. (2009). Neuropsychological deficits in relation to symptoms of ADHD: Independent contributions and interactions. Child Neuropsychology, 15(3), 262–279. Scholar
  59. Weigard, A., Huang-Pollock, C., Brown, S., & Heathcote, A. (2018). Testing formal predictions of neuroscientific theories of ADHD with a cognitive model–based approach. Journal of Abnormal Psychology, 127(5), 529–539. Scholar
  60. Wolfers, T., Onnink, A. M., Zwiers, M. P., Arias-Vasquez, A., Hoogman, M., Mostert, J. C., Kan, C. C., Slaats-Willemse, D., Buitelaar, J. K., & Franke, B. (2015). Lower white matter microstructure in the superior longitudinal fasciculus is associated with increased response time variability in adults with attention-deficit/ hyperactivity disorder. Journal of Psychiatry & Neuroscience, 40(5), 344–351. Scholar
  61. Wu, Y. Y., Huang, Y. S., Chen, Y. Y., Chen, C. K., Chang, T. C., & Chao, C. C. (2007). Psychometric study of the test of variables of attention: Preliminary findings on Taiwanese children with attention-deficit/hyperactivity disorder. Psychiatry and Clinical Neurosciences, 61(3), 211–218. Scholar
  62. Youngwirth, S. D., Harvey, E. A., Gates, E. C., Hashim, R. L., & Friedman-Weieneth, J. L. (2007). Neuropsychological abilities of preschool-aged children who display hyperactivity and/or oppositional-defiant behavior problems. Child Neuropsychology, 13, 422–443. Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Division of Clinical Psychology, Graduate Institute of Behavioral Sciences, College of MedicineChang Gung UniversityTaoyuanTaiwan
  2. 2.Department of Child PsychiatryChang Gung Memorial Hospital at LinkouTaoyuanTaiwan
  3. 3.Department of PsychiatryNational Taiwan University Hospital, and College of MedicineTaipeiTaiwan

Personalised recommendations