Provenance of correlations in psychological data

Two distinct families of statistical processes are considered in the production of psychophysical time series data (Gilden, 1997, 2001; Gilden, Thornton, & Mallon, 1995). We inquire whether the spectral signatures of the underlying dynamics are better described in terms of short-range autoregressive moving-average (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.