Automatic and controlled stimulus processing in conflict tasks: Superimposed diffusion processes and delta functions

•A model framework for conflict tasks is provided.•The model is based on diffusion processes.•Superposition of controlled and automatic processes.•The model accounts for all observed shapes of delta functions.•Speed of automatic processes determines the shape of delta functions.

An elaborated diffusion process model (a Diffusion Model for Conflict Tasks, DMC) is introduced that combines conceptual features of standard diffusion models with the notion of controlled and automatic processes. DMC can account for a variety of distributional properties of reaction time (RT) in conflict tasks (e.g., Eriksen flanker, Simon, Stroop). Specifically, DMC is compatible with all observed shapes of delta functions, including negative-going delta functions that are particularly challenging for the class of standard diffusion models. Basically, DMC assumes that the activations of controlled and automatic processes superimpose to trigger a response. Monte Carlo simulations demonstrate that the unfolding of automatic activation in time largely determines the shape of delta functions. Furthermore, the predictions of DMC are consistent with other phenomena observed in conflict tasks such as error rate patterns. In addition, DMC was successfully fitted to experimental data of the standard Eriksen flanker and the Simon task. Thus, the present paper reconciles the prominent and successful class of diffusion models with the empirical finding of negative-going delta functions.