Advertisement

The Mismatch of Intrinsic Fluctuations and the Static Assumptions of Linear Statistics

  • Mary Jean Amon
  • John G. Holden
Article
  • 27 Downloads

Abstract

The social and cognitive science replication crisis is partly due to the limitations of commonly used statistical tools. Inferential statistics require that unsystematic measurement variation is independent of system history, and weak relative to systematic or causal sources of variation. However, contemporary systems research underscores the dynamic, adaptive nature of social, cognitive, and behavioral systems. Variation in human activity includes the influences of intrinsic dynamics intertwined with changing contextual circumstances. Conventional inferential techniques presume milder forms of variability, such as unsystematic measurement error, as in a Gaussian distribution. Inferential statistics indicate an elementary Newtonian cause-effect metaphor for change that is inconsistent with known principles of change in complex systems. Pattern formation in self-organizing systems and quantum probability are used to illustrate theoretical metaphors that instantiate alternative notions of change in complex systems. Inferential statistics and related techniques are crucial scientific resources. However, in the social and behavioral sciences, they must be practiced in conjunction with an appropriate general systems framework that accommodates intrinsic fluctuations and contextual adaptation.

Notes

References

  1. Aks, D.J., G.J. Zelinsky, and J.C. Sprott. 2002. Memory across eye-movements: 1/ƒα dynamic in visual search. Nonlinear Dynamics, Psychology, and Life Sciences 6: 1–25.  https://doi.org/10.1167/1.3.230.CrossRefGoogle Scholar
  2. Amon, M.J., and J.G. Holden. 2016. Fractal scaling and implicit bias: A conceptual replication of Correll (2008). In Proceedings of the 38th Annual Conference of the Cognitive Science Society, ed. A. Papafragou, D. Grodner, D. Mirman, and J.C. Trueswell, 1553–1558. Philadelphia: Cognitive Science Society.Google Scholar
  3. Amon, M.J., O. Pavlov, and J.G. Holden. 2018. Synchronization and fractal scaling as resources for cognitive control. Cognitive Systems Research.  https://doi.org/10.1016/j.cogsys.2018.04.010.
  4. Andrews, S., and A. Heathcote. 2001. Distinguishing common and task-specific processes in word identification: A matter of some moment? Journal of Experimental Psychology: Human Perception and Performance 27: 514–544.  https://doi.org/10.1037//0278-7393.27.2.514.CrossRefGoogle Scholar
  5. Atmanspacher, H., H. Römer, and H. Walach. 2002. Weak quantum theory: Complementarity and entanglement in physics and beyond. Foundations of Physics 32: 379–406.CrossRefGoogle Scholar
  6. Ausloos, M., P. Clippe, and C. Laurent. 1990. Homogenous and fractal behavior of superconducting fluctuations in the electrical resistivity of granular ceramic superconductors. Physical Review B 41: 9509–9509.CrossRefGoogle Scholar
  7. Bak, P. 1996. How nature works: The science of self-organized criticality. New York: Springer.CrossRefGoogle Scholar
  8. Baken, R.J. 1990. Irregularity of vocal period and amplitude: A first approach to the fractal analysis of voice. Journal of Voice 4: 185–197.  https://doi.org/10.1016/S0892-1997(05)80013-X.CrossRefGoogle Scholar
  9. Balota, D.A., and J.I. Chumbley. 1984. Are lexical decisions a good measure of lexical access? The role of word frequency in the neglected decision stage. Journal of Experimental Psychology: Human Perception and Performance 10: 340–357.  https://doi.org/10.1037//0096-1523.10.3.340.CrossRefGoogle Scholar
  10. Balota, D.A., and D.H. Spieler. 1999. Word frequency, repetition, and lexicality effects in word recognition tasks: Beyond measures of central tendency. Journal of Experimental Psychology: General 128: 32–55.  https://doi.org/10.1037/0096-3445.128.1.32.CrossRefGoogle Scholar
  11. Benjamin, D.J., J.O. Berger, M. Johannesson, B.A. Nosek, E.J. Wagenmakers, R. Berk, et al. 2018. Redefine statistical significance. Nature Human Behaviour 2 (1): 6–10.CrossRefGoogle Scholar
  12. Blank, M., and R. Goodman. 2011. DNA is a fractal antenna in electromagnetic fields. International Journal of Radiation Biology 87: 409–415.  https://doi.org/10.3109/09553002.2011.538130.CrossRefGoogle Scholar
  13. Camazine, S., N.R. Franks, J. Sneyd, E. Bonabeau, J.-L. Deneubourg, and G. Theraulaz. 2001. Self-organization in biological systems. Princeton: Princeton University Press.Google Scholar
  14. Di leva, A., F. Grizzi, H. Jelinek, A.J. Pellionisz, and G.A. Losa. 2013. Fractals in the neurosciences, part I: General principles and basic neurosciences. Neuroscientist 20: 403–417.  https://doi.org/10.1177/1073858413513927.CrossRefGoogle Scholar
  15. Digman, J.M. 1990. Personality structure: Emergence of the five-factor model. Annual Review of Psychology 41: 417–440.  https://doi.org/10.1146/annurev.ps.41.020190.002221.CrossRefGoogle Scholar
  16. Efron, B., and R.J. Tibshirani. 1993. An introduction of the bootstrap. New York: Chapman & Hall.CrossRefGoogle Scholar
  17. Favela, L.H., C.A. Coey, E.R. Griff, and M.J. Richardson. 2016. Fractal analysis reveals subclasses of neurons and suggests an explanation of their spontaneous activity. Neuroscience Letters 626: 54–58.  https://doi.org/10.1016/j.neulet.2016.05.017.CrossRefGoogle Scholar
  18. Flach, J.M., S. Dekker, and P.J. Stappers. 2007. Playing twenty questions with nature (the surprise version): Reflections on the dynamics of experience. Theoretical Issues in Ergonomics Science 9 (2): 125–154.  https://doi.org/10.1080/14639220601095353.CrossRefGoogle Scholar
  19. Forster, K. I., & Forster, J. C. 1996. DMASTR (version 2.16) [computer program]. Available at http://www.u.arizona.edu/~kforster/dmastr/dmastr.htm. Retrieved 9/1/1996
  20. Fraiman, D., P. Balenzuela, J. Foss, and D.R. Chialvo. 2009. Ising-like dynamics in large-scale functional brain networks. Physical Review E 79 (6): 061922.CrossRefGoogle Scholar
  21. Free, S.L., S.M. Sisodiya, J.J. Cook, D.R. Fish, and S.D. Shorvon. 1996. Three-dimensional fractal analysis of the white matter surface from magnetic resonance images of the human brain. Cerebral Cortex 6: 830–836.CrossRefGoogle Scholar
  22. Frette, V., K. Christensen, A. Malthe-Sørenssen, J. Feder, T. Jøssang, and P. Meakin. 1996. Avalanche dynamics in a pile of rice. Nature 379: 49–52.CrossRefGoogle Scholar
  23. Friedman, J., Hastie, T., & Tibshirani, R. 2009. The elements of statistical learning: Data mining, inference, and prediction. Springer series in statistics. Retrieved from http://www-stat.stanford.edu/~tibs/ElemStatLearn/.
  24. Gabora, L., and D. Aerts. 2002. Contextualizing concepts using a mathematical generalization of the quantum formalism. Journal of Experimental and Theoretical Artificial Intelligence 14: 327–358.  https://doi.org/10.1080/09528130210162253.CrossRefGoogle Scholar
  25. Gould, S.J. 1996. The mismeasure of man. New York: WW Norton & Company.Google Scholar
  26. Guastello, S.J., M.E. Koopmans, and D.E. Pincus. 2009. Chaos and complexity in psychology: The theory of nonlinear dynamical systems. Cambridge: Cambridge University Press.Google Scholar
  27. Handel, P.H., and A.L. Chung. 1993. Noise in physical systems and 1/"f" fluctuations. New York: American Institute of Physics.Google Scholar
  28. Hasselman, F. 2015. Beyond the boundary. An analysis of verisimilitude and causal ontology of scientific claims: Etiologies of developmental dyslexia as a case in point (Unpublished doctoral dissertation). Radboud University Nijmegen, Netherlands. Retrieved from  https://doi.org/10.6084/m9.figshare.928517.
  29. Head, M.L., L. Holman, R. Lanfear, A.T. Kahn, and M.D. Jennions. 2015. The extent and consequences of p-hacking in science. PLoS Biology 13: e1002106.  https://doi.org/10.1371/journal.pbio.1002106.CrossRefGoogle Scholar
  30. Holden, J.G. 2002. Fractal characteristics of response time variability. Ecological Psychology 14: 53–86.CrossRefGoogle Scholar
  31. Holden, J.G., and S. Rajaraman. 2012. The self-organization of a spoken word. Frontiers in Psychology 3: 1–24.  https://doi.org/10.3389/fpsyg.2012.00209.CrossRefGoogle Scholar
  32. Holden, J.G., G. Van Orden, and M.T. Turvey. 2009. Dispersion of response times reveals cognitive dynamics. Psychological Review 116: 318–342.  https://doi.org/10.1037/a0014849.CrossRefGoogle Scholar
  33. Holden, J.G., I. Choi, P.G. Amazeen, and G. Van Orden. 2011. Fractal 1/ƒ dynamics suggest entanglement of measurement and human performance. Journal of Experimental Psychology: Human Perception & Performance 37: 935–948.  https://doi.org/10.1037/a0020991.CrossRefGoogle Scholar
  34. Holden, J.G., J.A. Riley, J. Gao, and K. Torre. 2013. Fractal analyses: Statistical and methodological innovations and best practices. Frontiers in Physiology 4: 97.  https://doi.org/10.3389/fphys.2013.00097.CrossRefGoogle Scholar
  35. Hollis, J., H. Kloos, and G. Van Orden. 2009. Origins of order in cognitive activity. In Chaos and complexity in psychology: The theory of nonlinear dynamical systems, ed. S.J. Guastello, M. Koopmans, and D. Pincus, 206–241. Cambridge: Cambridge University Press.Google Scholar
  36. Huey, E.B. 1908. The psychology and pedagogy of reading. New York: MacMillan.Google Scholar
  37. Ioannidis, J.P.A. 2005. Why most published research findings are false. PLoS Medicine 2: e124.  https://doi.org/10.1371/journal.pmed.0020124.CrossRefGoogle Scholar
  38. Jensen, H.J. 1998. Self-organized criticality: Emergent complex behavior in physical and biological systems. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  39. Kauffman, S. 1995. At home in the universe: The search for the laws of self-organization and complexity. New York: Oxford University Press.Google Scholar
  40. Kello, C.T. 2013. Critical branching neural networks. Psychological Review 120: 230–254.  https://doi.org/10.1037/a0030970.CrossRefGoogle Scholar
  41. Kello, C.T., G.D.A. Brown, R. Ferrer-i-Cancho, J. Holden, K. Linkenkaer-Hansen, T. Rhodes, and G.C. Van Orden. 2010. Scaling laws in cognitive sciences. Trends in Cognitive Sciences 14: 223–232.  https://doi.org/10.1016/j.tics.2010.02.005.CrossRefGoogle Scholar
  42. Kelso, S. 1995. Dynamic patterns: The self-organization of brain and behavior. Cambridge: MIT Press.Google Scholar
  43. Killeen, P.R. 2005. An alternative to null-hypothesis significance tests. Psychological Science 16: 345–353.CrossRefGoogle Scholar
  44. Klein, J.L. 1997. Statistical visions in time: A history of time series analysis. New York: Cambridge University Press.Google Scholar
  45. Konvalinka, I., D. Xygalatas, J. Bulbulia, U. Schojødt, E.-M. Jegindø, S. Wallot, G. Van Orden, and A. Roepstorff. 2011. Synchronized arousal between performers and related spectators in a fire-walking ritual. Proceedings of the National Academy of Sciences 108: 8514–8519.  https://doi.org/10.1073/pnas.1016955108.CrossRefGoogle Scholar
  46. Kučera, H., and W.N. Francis. 1967. Computational analysis of present-day American English. Providence: Brown University Press.Google Scholar
  47. Kugler, P.N., and M.T. Turvey. 1987. Information, natural law and the self-assembly of rhythmic movement. Hillsdale: Erlbaum.Google Scholar
  48. Lakoff, G. 1987. Women, fire and dangerous things: What categories reveal about thought.Google Scholar
  49. Luce, R.D. 1986. Response times: Their role in inferring elementary mental organization. New York: Oxford University Press.Google Scholar
  50. Mäkikallio, T.H., H.V. Huikuri, A. Makikallio, L.B. Sourander, R.D. Mitrani, A. Castellanos, and R.J. Myerburg. 2001. Prediction of sudden cardiac death by fractal analysis of heart rate variability in elderly subjects. Journal of the American College of Cardiology 37: 1395–1402.CrossRefGoogle Scholar
  51. Mandelbrot, B.B. 1983. The fractal geometry of nature. San Francisco: W. H. Freeman and Company.CrossRefGoogle Scholar
  52. Mitchell, J. 2014. On the emptiness of failed replications. Retrieved from http://wjh.harvard.edu/~jmitchel/writing/failed_science.htm
  53. Mogiliansky, A.L., S. Zamir, and H. Zwirn. 2009. Type indeterminacy: A model of the KT (Kahneman–Tversky)-man. Journal of Mathematical Psychology 53 (5): 349–361.CrossRefGoogle Scholar
  54. Open Science Collaboration. 2015. Estimating the reproducibility of psychological science. Science 349: aac4716.  https://doi.org/10.1126/science.aac4716.CrossRefGoogle Scholar
  55. Peng, C.-K., S. Havlin, J.M. Hausdorff, J.E. Mietus, H.E. Stanley, and A.L. Goldberger. 1995. Fractal mechanisms and heart rate dynamics: Long-range correlations and their breakdown with disease. Journal of Electrocardiology 28: 59–65.CrossRefGoogle Scholar
  56. Press, W.H. 1978. Flicker noises in astronomy and elsewhere. Comments on Astrophysics 7 (4): 103–119.Google Scholar
  57. Ratcliff, R. 1978. A theory of memory retrieval. Psychological Review 85: 59–108.  https://doi.org/10.1037/0033-295X.85.2.59.CrossRefGoogle Scholar
  58. Ratcliff, R. 1979. Group reaction time distributions and an analysis of distribution statistics. Psychological Bulletin 86: 446–461.CrossRefGoogle Scholar
  59. Ratcliff, R., P. Gomez, and G. McKoon. 2004. A diffusion model account of the lexical decision task. Psychological Review 111: 159–182.  https://doi.org/10.1037/0033-295X.111.1.159.CrossRefGoogle Scholar
  60. Riley, M.A., and J.G. Holden. 2012. Dynamics of cognition. Wiley Interdisciplinary Reviews: Cognitive Science 3: 593–606.CrossRefGoogle Scholar
  61. Rubalcaba, J.J.O. 1997. Fractal analysis of climatic data: Annual precipitation records in Spain. Theoretical and Applied Climatology 56: 83–87.CrossRefGoogle Scholar
  62. Rubin, D.B. 1981. The Bayesian bootstrap. The Annals of Statistics 9: 130–134.  https://doi.org/10.1214/aos/1176345338.CrossRefGoogle Scholar
  63. Sapolsky, R., and S. Balt. 1996. Reductionism and variability in data: A meta-analysis. Perspectives in Biology and Medicine 39: 193–203.CrossRefGoogle Scholar
  64. Scafetta, N., L. Griffin, and B.J. West. 2003. Holder exponent spectra for human gait. Physica A: Statistical Mechanics and its Applications 328: 561–583.  https://doi.org/10.1016/S0378-4371(03)00527-2.CrossRefGoogle Scholar
  65. Schmiedek, F., K. Oberauer, O. Wilhelm, H.M. Süß, and W.W. Wittmann. 2007. Individual differences in components of reaction time distributions and their relations to working memory and intelligence. Journal of Experimental Psychology: General 136: 414–429.  https://doi.org/10.1037/0096-3445.136.3.414.CrossRefGoogle Scholar
  66. Schwarz, W. 2001. The ex-Wald distribution as a descriptive model of response times. Behavior Research Methods, Instruments, & Computers 33: 457–469.CrossRefGoogle Scholar
  67. Shanon, B. 1993. The representational and the presentational: An essay on cognition and the study of the mind. New York: Harvester Wheatsheaf.Google Scholar
  68. Stambolieva, K. 2011. Fractal properties of postural sway during quiet stance with changed visual and proprioceptive inputs. Journal of Physiological Science 61: 123–130.  https://doi.org/10.1007/s12576-010-0129-4.CrossRefGoogle Scholar
  69. Stephen, D.G., and J.A. Dixon. 2008. The self-organization of insight: Entropy and power laws in problem solving. The Journal of Problem Solving 2: 72–101.  https://doi.org/10.7771/1932-6246.1043.CrossRefGoogle Scholar
  70. Stephen, D.G., and G.C. Van Orden. 2012. Searching for general principles in cognitive performance: Reply to commentators. Topics in Cognitive Science 4: 94–102.  https://doi.org/10.1111/j.1756-8765.2011.01171.x.CrossRefGoogle Scholar
  71. Stone, G.O., and G.C. Van Orden. 1989. Are words represented by nodes? Memory & Cognition 17: 511–524.  https://doi.org/10.3758/BF03197073.CrossRefGoogle Scholar
  72. Stone, G.O., and G.C. Van Orden. 1993. Strategic control of processing in word recognition. Journal of Experimental Psychology: Human Perception and Performance 19: 744–774.  https://doi.org/10.1037/0096-1523.19.4.744.CrossRefGoogle Scholar
  73. Thelen, E., and L.B. Smith. 1994. A dynamic systems approach to the development of cognition and action. Cambridge: MIT Press.Google Scholar
  74. Townsend, J.T., and F.G. Ashby. 1983. The stochastic modeling of elementary psychological processes. Cambridge: Cambridge University Press.Google Scholar
  75. Tschacher, W., and J.P. Dauwalder. 2003. The dynamical systems approach to cognition. New Jersey: World Scientific.CrossRefGoogle Scholar
  76. Uttal, W.R. 1990. On some two-way barriers between models and mechanisms. Perception & Psychophysics 48: 188–203.  https://doi.org/10.3758/BF03207086.CrossRefGoogle Scholar
  77. Uttal, W.R. 2001. The new phrenology: The limits of localizing cognitive processes in the brain. Cambridge: MIT Press.Google Scholar
  78. Van Orden, G.C., and J.G. Holden. 2002. Intentional contents and self-control. Ecological Psychology 14: 87–109.  https://doi.org/10.1080/10407413.2003.9652753.CrossRefGoogle Scholar
  79. Van Orden, G.C., M.A. Jansen op Haar, and A.M.T. Bosman. 1997. Complex dynamic systems also predict dissociations, but they do not reduce to autonomous components. Cognitive Neuropsychology 14: 131–165.  https://doi.org/10.1080/026432997381646.CrossRefGoogle Scholar
  80. Van Orden, G.C., J.G. Holden, M.N. Podgonik, and C.S. Aitchison. 1999. What swimming says about reading: Coordination, context and homophone errors. Ecological Psychology 11: 45–79.  https://doi.org/10.1207/s15326969eco1101_2.CrossRefGoogle Scholar
  81. Van Orden, G.C., B.F. Pennington, and G.O. Stone. 2001. What do double dissociations prove? Cognitive Science 25: 111–172.  https://doi.org/10.1207/s15516709cog2501_5.CrossRefGoogle Scholar
  82. Van Orden, G.C., J.G. Holden, and M.T. Turvey. 2003. Self-organization of cognitive performance. Journal of Experimental Psychology: General 132: 331–350.  https://doi.org/10.1037/0096-3445.132.3.331.CrossRefGoogle Scholar
  83. Van Orden, G.C., J.G. Holden, and M.T. Turvey. 2005. Human cognition and 1/ƒα scaling. Journal of Experimental Psychology: General 134: 117–123.  https://doi.org/10.1037/0096-3445.134.1.117.CrossRefGoogle Scholar
  84. Van Orden, G.C., C.T. Kello, and J.G. Holden. 2010. Situated behavior and the place of measurement in psychological theory. Ecological Psychology 22: 24–43.  https://doi.org/10.1080/10407410903493145.CrossRefGoogle Scholar
  85. Van Orden, G., G. Hollis, and S. Wallot. 2012. The blue-collar brain. Frontiers in Physiology 3 (207).  https://doi.org/10.3389/fphys.2012.00207.
  86. van Rooij, M., and J.G. Holden. 2013. Correspondence are cognitive functions localizable? Response. Journal of Economic Perspectives 27 (2): 250–252.Google Scholar
  87. van Rooij, M.M., B.A. Nash, S. Rajaraman, and J.G. Holden. 2013. A fractal approach to dynamic inference and distribution analysis. Frontiers in Physiology 4: 1–16.  https://doi.org/10.3389/fphys.2013.00001.CrossRefGoogle Scholar
  88. Verhagen, J., and E.-J. Wagenmakers. 2014. Bayesian tests to quantify the results of a replication attempt. Journal of Experimental Psychology: General 143: 1457–1475.  https://doi.org/10.1037/a0036731.CrossRefGoogle Scholar
  89. Wagenmakers, E.-J., R. Wetzels, D. Borsboom, and H.L.J. van der Maas. 2011. Why psychologists must change the way they analyze their data: The case of psi: Comment on Bem (2011). Journal of Personality and Social Psychology 100: 426–432.  https://doi.org/10.1037/a0022790.CrossRefGoogle Scholar
  90. Wallot, S., and D.G. Kelty-Stephen. 2017. Interaction-dominant causation in mind and brain, and its implication for questions of generalization and replication. Minds and Machines 28: 353–374.  https://doi.org/10.1007/s11023-017-9455-0.CrossRefGoogle Scholar
  91. Wan, S., Q. Liu, J. Zou, and W. He. 2016. Nonlinearity and fractal properties of climate change during the past 500 years in northwestern China. Discrete Dynamics in Nature and Society 2016: 1–7.  https://doi.org/10.1155/2016/4269431.CrossRefGoogle Scholar
  92. Wang, Z., T. Solloway, R.M. Shiffrin, and J.R. Busemeyer. 2014. Context effects produced by question orders reveal quantum nature of human judgments. Proceedings of the National Academy of Sciences 111: 9431–9436.  https://doi.org/10.1073/pnas.1407756111.CrossRefGoogle Scholar
  93. Watkins, M.J. 1990. Mediationism and the obfuscation of memory. American Psychologist 45: 328–335.  https://doi.org/10.1037//0003-066X.45.3.328.CrossRefGoogle Scholar
  94. Wijnants, M.L. 2014. A review of theoretical perspectives in cognitive science on the presence of scaling in coordinated physiological and cognitive processes. Journal of Nonlinear Dynamics 2014: 962043.  https://doi.org/10.1155/2014/962043.CrossRefGoogle Scholar
  95. Yates, F.E. 1987. Self-organizing systems: The emergence of order. New York: Plenum Press.CrossRefGoogle Scholar
  96. Yu, L., Grebogi, C., & Ott, E. 1989. Fractal structure in physical space in the dispersal of particles in fluids. In L. Lam & H. C. Morris. Nonlinear Structures in Physical Systems: Pattern Formation, Chaos, and Waves (223–231). Proceedings of the Second Woodward Conference: San Jose State University.Google Scholar
  97. Zhao, G., K. Denisova, P. Sehatpour, J. Long, W. Gui, J. Qiao, D.C. Javitt, and Z. Wang. 2016. Fractal dimension analysis of subcortical gray matter structures in schizophrenia. PLoS ONE 11 (5): e0155415.  https://doi.org/10.1371/journal.pone.0155415.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Psychological and Brain SciencesIndiana University BloomingtonBloomingtonUSA
  2. 2.Complexity GroupUniversity of CincinnatiCincinnatiUSA

Personalised recommendations