Chapter 5 discusses core experimental findings in the evaluation of sequential-sampling decision models. It compares the response time and accuracy predictions of Wiener and Ornstein–Uhlenbeck (OU) diffusion models to those of the Vickers accumulator and Poisson counter models on three representative data sets. It highlights the relative invariance of the shapes of empirical response time distributions as a function of changes in task difficulty and speed versus accuracy instructions, along with changes in the ordering of distributions for correct responses and errors. The chapter emphasizes that the shape-invariance of empirical response time distributions arises naturally from diffusion models, but is difficult for other models to predict. The OU model, which adds decay to the drift rate of the process, has been advocated on the grounds of neural plausibility, because it represents bounded evidence accumulation. However, an OU model with moderate decay makes predictions that are empirically indistinguishable from those of the Wiener diffusion model and an OU model with large decay predicts response time distributions that are more skewed than are found in data. Empirically, the best-fitting model is the Wiener diffusion model.

Chapter 3 describes the variety of sequential-sampling models of decision making that have been proposed in the literature and situates diffusion process models among them. The chapter provides a taxonomy of model types, in which models are classified according to their stopping rule and whether evidence is accumulated in discrete or continuous amounts in discrete or continuous time. Historically important models have been the recruitment model, the Vickers accumulator model, the Poisson counter model, and several random walk models, including one that implements the sequential probability ratio test, which accumulates the log-likelihood ratios of the evidence states. The Wiener diffusion process assumes that evidence is continuously distributed and accumulated in continuous time, and that decisions are made using a relative stopping rule. The chapter describes two alternative ways to characterize diffusion processes mathematically and obtain predictions for them, which are evaluated in Chapter 5: one using partial differential equations and the other using stochastic differential equations.