Provenance of correlations in psychological data

Abstract

Two distinct families of statistical processes are considered in the production of psychophysical time series data (Gilden, 1997(Gilden, , 2001Gilden, Thornton, & Mallon, 1995). We inquire whether the spectral signatures of the underlying dynamics are better described in terms of short-range autoregressive movingaverage (ARMA) processes or long-range fractal processes. A thorough presentation of both families is given so as to clarify the scope and generalizability of the models as descriptions of choice reaction time data. Analyses of data are supplemented by the construction of a spectral likelihood classifier that discriminates between the two families of processes. The classifier has sufficient sensitivity to ensure that fractals are correctly identified and that ARMA processes will rarely be misconstrued as belonging to the fractal family. Spectral likelihood classification illustrates an extremely general framework for testing competing spectral hypotheses and is offered for use in measuring the specific character of fluctuations in designed experiments.

Detecting and predicting changes

“…When the optimal strategy in a task is to provide a series of independent and identically distributed responses, people often perform sub-optimally. Long-range autocorrelations have been observed, where responses depend on earlier events that occurred quite a long time previously (e.g., Gilden, 2001; Thornton & Gilden, 2005;Van Orden, Holden, & Turvey, 2003, although not all authors agree on the meaning of the phenomena (e.g., Farrell, Wagenmakers, & Ratcliff, 2006;Wagenmakers, Farrell, & Ratcliff, 2004. The same criticism applies to dynamical systems research as to the Gambler's Fallacy-tasks requiring long sequences of stationary and conditionally random responses have questionable ecological validity.…”

Dynamics of cognition

“…98,102,103 The bulk of that initial skepticism was answered, however. 44,104 The empirical patterns held up to rigorous statistical scrutiny, and fractal scaling, in one form or another, has emerged as the most representative and most likely description of the empirical reports. 105,106 The patterns of 1/f scaling expressed in physical systems are typically relatively stable over time.…”

The Pervasiveness of 1/f Scaling in Speech Reflects the Metastable Basis of Cognition

“…Therefore, high-frequency whitening does not undermine a 1/f scaling conclusion, but it does complicate estimation of the 1/f α scaling exponent. To account for high-frequency whitening, Thornton and Gilden (2005) developed a method for fitting a "fractional Brownian motion plus white noise" (fBmW) model to time series data averaged in the frequency domain (fractional Brownian motion corresponds to 1/f α scaling with variable α). The two free parameters are the 1/f scaling exponent (α) and the amplitude of white noise (β), and the model allows one to estimate α while accounting for whitening with β.…”