Adjusting behavioral methods when applying nonlinear dynamical measures to stimulus rate

A nonlinear dynamical perspective addresses an area of behavior that tends to be ignored: trial-to-trial variability under seemingly identical conditions. Data exhibiting sequence effects are excellent candidates for a nonlinear dynamical analysis, because of their dependence on previous trial events. When applying nonlinear dynamical tools to behavioral data, the assumptions underlying the tools may require changes in experimental methodology. In this paper, the assumptions of trial timing and their potential impact on nonlinear dynamical analysis are explored. This is done with the intent of initiating a discussion on the appropriate control of trial timing. To examine these issues, each participant's response times on simple two-choice tasks were treated as a time series and submitted along with two comparisons to two nonlinear dynamical measures. Two experimental variables, stimulus rate and stimulus-response mapping, were manipulated in order to examine the issue of controlling trial timing via stimulus rate. Significant differences between the observed and comparison time series were found for estimated dimensionalities(m). Differences in dimensionality(m) estimates were also found between the experimental variables. Of the two methods for controlling stimulus rate, response-stimulus-interval and inter-stimulus-interval, the latter is recommended when applying nonlinear dynamical measures.