Estimation and interpretation of 1/f a noise in human cognition

In the vast majority of experiments in cognitive psychology, any information about the order in which empirical observations are obtained is discarded. The implicit assumption of this approach is that performance on successive trials is not correlated and, hence, any variance unaccounted for by the experimental manipulations can be considered random noise. In this article, we study human performance in cognitive tasks from a quite different perspective, focusing on how performance fluctuates over time (cf. Gilden, 2001). In this time-series approach to human cognition, the order in which observations are obtained is not neglected but, in fact, provides the data of interest. Thus, we seek to study the extent to which current behavior can be explained on the basis of past behavior (or, alternatively, the extent to which we can predict future behavior). In addition, the specific manner in which serial correlations decrease as the number of intervening trials increases can provide information about underlying cognitive mechanisms. Several researchers in cognitive psychology have studied serial correlations in human performance (e.g., Merrill & Bennett, 1956; Verplanck, Collier, & Cotton, 1952; Weiss, Coleman, & Green, 1955). In particular, Laming (1968) reported and modeled the serial dependency structure of response times (RTs) in two-choice experiments. Laming (1968) found that RTs on contiguous trials were positively correlated, so that a relatively short RT tended to be followed by another relatively short RT. These serial correlations decayed with increasing separation between trials (i.e., lag), so that there was evidence of significant serial correlations only up to a lag of six or seven. The fast decay of these serial correlations is consistent with other work (e.g., Laming, 1979a) that has found serial correlations to be small and transient (or even nonexistent—e.g., Busey & Townsend, 2001; Townsend, Hu, & Kadlec, 1988). However, the popular belief that serial correlations in human performance are small and transient has recently been challenged. Specifically, it has been reported that the pattern of serial correlations in human performance