Advertisement

Theoretical models of reaction times arising from simple-choice tasks

  • Mauricio TejoEmail author
  • Héctor Araya
  • Sebastián Niklitschek-Soto
  • Fernando Marmolejo-Ramos
Brief Communication

Abstract

In this work we present a group of theoretical models for reaction times arising from simple-choice task tests. In particular, we argue for the inclusion of a shifted version of the Gamma distribution as a theoretical model based on a mathematical result on first hitting times. We contrast the goodness-of-fit of those models with the Ex-Gaussian distribution, using data from recently published experiments. The evidence of the results obtained highlights the convenience of proposing theoretical models for reaction times instead of models acting exclusively as quantitative distribution measurements.

Keywords

Cognitive process Reaction times Quantitative distribution measurements Theoretical models Simple-choice task tests 

Notes

Acknowledgements

This work is supported by funding from Project FONDECYT 1161023. We thank Carlos Velasco and David C. Osmon for providing us with the data sets featured here. The authors thank Professor Jeff Miller for assisting in clarifying definitions of simple-choice and 2AFC tasks. We also thank Nathan Leigh Jones and Amy K. Robinson for proofreading this manuscript. The authors acknowledge the unknown referees for their insightful suggestions.

References

  1. Anders R, Alario F-X, Van Maanen L (2016) The shifted Wald distribution for response time data analysis. Psychol Methods 21(3):309–327CrossRefGoogle Scholar
  2. Balota DA, Yap MJ (2011) Moving beyond the mean in studies of mental chronometry: the power of response time distributional analyses. Curr Dir Psychol Sci 20:160–166CrossRefGoogle Scholar
  3. Blurton SP, Kesselmeier M, Gondana M (2017) The first-passage time distribution for the diffusion model with variable drift. J Math Psychol 76:7–12CrossRefGoogle Scholar
  4. Brown SD, Heathcote A (2008) The simplest complete model of choice response time: linear ballistic accumulation. Cognit Psychol 57(3):153–178CrossRefGoogle Scholar
  5. Campitelli G, Macbeth G, Ospina R, Marmolejo-Ramos F (2017) Three strategies for the critical use of statistical methods in psychological research. Edu Psychol Meas 77(5):881–895CrossRefGoogle Scholar
  6. Donkin C, Brown S (2018) Response times and decision-making. In: Wixted JT (ed) Steven’s handbook of experimental psychology and cognitive science. Wiley, HobokenGoogle Scholar
  7. El-Taha M (1993) Mvu estimation in a shifted gamma distribution with shape parameter a known integer: Mvu estimation in a shifted gamma distribution. Commun Stat Simul Comput 22(3):831–843CrossRefGoogle Scholar
  8. Horrocks J, Thomson M (2004) Modeling event times with multiple outcomes using the Wiener process with drift. Lifetime Data Anal 10(1):29–49CrossRefGoogle Scholar
  9. Jackson K, Kreinin A, Zhang W (2009) Randomization in the first hitting time problem. Stat Probab Lett 79(23):2422–2428CrossRefGoogle Scholar
  10. Kim S, Lee JY, Sung DK (2003) A shifted gamma distribution model for long-range dependent internet traffic. IEEE Commun Lett 7(3):124–126CrossRefGoogle Scholar
  11. LaBerge D (1962) A recruitment theory of simple behavior. Psychometrika 27(4):375–396CrossRefGoogle Scholar
  12. Marmolejo-Ramos F, Cousineau D, Benites L, Maehara R (2015) On the ecacy of procedures to normalize Ex-Gaussinan distributions. Front Psychol 5:1548CrossRefGoogle Scholar
  13. Marmolejo-Ramos F, Gonzalez-Burgos J (2013) A power comparison of various tests of univariate normality on Ex-Gaussian distributions. Methodology 9(4):137–149CrossRefGoogle Scholar
  14. Marmolejo-Ramos F, Velez JI, Romao X (2015) Automatic outlier detection via the Ueda method. J Stat Distrib Appl 2:8CrossRefGoogle Scholar
  15. Massaro DW (1989) Experimental psychology: an information processing approach. Harcourt Brace Jovanovich, San DiegoGoogle Scholar
  16. Matzke D, Wagenmakers EJ (2009) Psychological interpretation of the ex-Gaussian and shifted Wald parameters: a diffusion model analysis. Psychon Bull Rev 16(5):798–817CrossRefGoogle Scholar
  17. McGill WJ, Gibbon J (1965) The general-gamma distribution and reaction times. J Math Psychol 2(1):1–18CrossRefGoogle Scholar
  18. McKenzie CR, Wixted JT, Noelle DC, Gyurjyan G (2001) Relation between confidence in yes-no and forced-choice tasks. J Exp Psychol Gen 130(1):140CrossRefGoogle Scholar
  19. Meyer DE, Osman AM, Irwin DE, Yantis S (1988) Modern mental chronometry. Biol Psychol 26(1–3):3–67CrossRefGoogle Scholar
  20. Nosek BA, Banaji MR (2001) The go/no-go association task. Soc Cognit 19(6):625–666CrossRefGoogle Scholar
  21. Osmon DC, Kazakov D, Santos O, Kassel MT (2018) Non-Gaussian distributional analyses of reaction times (RT): improvements that increase efficacy of RT tasks for describing cognitive processes. Neuropsychol Rev.  https://doi.org/10.1007/s11065-018-9382-8 Google Scholar
  22. Palmer EM, Horowitz Todd S, Torralba A, Wolfe JM (2011) What are the shapes of response time distributions in visual search? J Exp Psychol 37(1):58Google Scholar
  23. Posner MI (2005) Timing the brain: mental chronometry as a tool in neuroscience. PLoS Biol 3(2):e51CrossRefGoogle Scholar
  24. Ratcliff R (1978) A theory of memory retrieval. Psychol Rev 85(2):59–108CrossRefGoogle Scholar
  25. Ratcliff R, Tuerlinckx F (2002) Estimating parameters of the diffusion model: approaches to dealing with contaminant reaction times and parameter variability. Psychon Bull Rev 9(3):438–481CrossRefGoogle Scholar
  26. Ratcliff R, Van Dongen HP (2011) Diffusion model for one-choice reaction-time tasks and the cognitive effects of sleep deprivation. Proc Natl Acad Sci 108(27):11285–11290CrossRefGoogle Scholar
  27. Ratcliff R, Voskuilen C, Teodorescu A (2018) Modeling 2-alternative forced-choice tasks: accounting for both magnitude and difference effects. Cognit Psychol 103:1–22CrossRefGoogle Scholar
  28. Rohrer D, Wixted JT (1994) An analysis of latency and interresponse time in free recall. Memory Cognit 22(5):511–524CrossRefGoogle Scholar
  29. Rousselet G, Wilcox R (2018) Reaction times and other skewed distributions: problems with the mean and the median. bioRxiv preprint first posted online Aug. 2, 2018,  https://doi.org/10.1101/383935
  30. Smith EE (1968) Choice reaction time: an analysis of the major theoretical positions. Psychol Bull 69(2):77–110CrossRefGoogle Scholar
  31. Tejo M, Niklitschek-Soto S, Marmolejo-Ramos F (2018) Fatigue-life distributions for reaction time data. Cognit Neurodyn 12:351–356CrossRefGoogle Scholar
  32. Usher M, Olami Z, McClelland JL (2002) Hick’s law in a stochastic race model with speed-accuracy tradeoff. J Math Psychol 46(6):704–715CrossRefGoogle Scholar
  33. Velasco C, Woods AT, Marks LE, Cheok AD, Spence C (2016) The semantic basis of taste-shape associations. Peer J 4:e1644CrossRefGoogle Scholar
  34. Velez JI, Correa JC, Marmolejo-Ramos F (2015) A new approach to the Box-Cox transformation. Front Appl Math Stat 1:12CrossRefGoogle Scholar
  35. Verbruggen F, Logan GD (2008) Automatic and controlled response inhibition: associative learning in the go/no-go and stop-signal paradigms. J Exp Psychol Gen 137(4):649–672CrossRefGoogle Scholar
  36. Wainer H (1977) Speed vs reaction time as a measure of cognitive performance. Memory Cognit 5(2):278–280CrossRefGoogle Scholar
  37. Wichmann F, Jäkel F (2018) Methods in psychophysics. In: Wixted JT (ed) Steven’s handbook of experimental psychology and cognitive science. Wiley, HobokenGoogle Scholar
  38. Woodrow H (1911) Reaction times. Psychol Bull 8(11):387–390CrossRefGoogle Scholar
  39. Woods DL, Wyma JM, Yund EW, Herron TJ, Reed B (2015) Factors influencing the latency of simple reaction time. Front Human Neurosci 9:131Google Scholar
  40. Yeshurun Y, Carrasco M, Maloney LT (2008) Bias and sensitivity in two-interval forced choice procedures: tests of the difference model. Vis Res 48(17):1837–1851CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Mauricio Tejo
    • 1
    Email author
  • Héctor Araya
    • 2
  • Sebastián Niklitschek-Soto
    • 3
  • Fernando Marmolejo-Ramos
    • 4
  1. 1.Departamento de MatemáticaUniversidad Tecnológica MetropolitanaSantiagoChile
  2. 2.Instituto de EstadísticaUniversidad de ValparaísoValparaísoChile
  3. 3.Facultad de Ciencias Físicas y MatemáticasUniversidad de ConcepciónConcepciónChile
  4. 4.School of PsychologyThe University of AdelaideAdelaideAustralia

Personalised recommendations