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The diffusion model for two-choice real-time decisions is applied to four psychophysical tasks. The model reveals how stimulus information guides decisions and shows how the information is processed through time to yield sometimes correct and sometimes incorrect decisions. Rapid two-choice decisions yield multiple empirical measures: response times for correct and error responses, the probabilities of correct and error responses, and a variety of interactions between accuracy and response time that depend on instructions and task difficulty. The diffusion model can explain all these aspects of the data for the four experiments we present. The model correctly accounts for error response times, something previous models have failed to do. Variability within the decision process explains how errors are made, and variability across trials correctly predicts when errors are faster than correct responses and when they are slower.Making decisions is a ubiquitous part of everyday life. In psychology, besides being an object of study in its own right, decision making plays a central role in the tasks used to study basic cognitive functions such as memory, perception, and language comprehension. Frequently, the decisions required in these tasks are rapid two-choice decisions, decisions that are based on information that can be described as varying along a single dimension. Two key features of these decisions are that they occur over time-decisions are never reached instantaneously-and that they are error prone. In this article, we present a model to explain this class of decision processes. The goal is to understand what information drives the decision and how the decision process evolves over time to reach correct and incorrect decisions. The problem is difficult because potential models are constrained to explain multiple empirical measures that interact in complex ways. The measures include mean response times for correct and error responses, the shapes of the distributions of the response times, and the probabilities of correct and error responses. The relation between response time and accuracy is not fixed; it varies according to whether speed or accuracy of performance is emphasized and according to whether one or the other of the responses is more probable or weighted more heavily. In addition, the relation between probability of an error and error response time is not fixed but varies across levels of overall accuracy. Because of these complexities, no previous model has been completely successful. Often, models have dealt with only one measure-accuracy but not response time, or response time but not accuracy. Models that have dealt with response time have usually tried to explain only mean response times for correct responses, not the shapes of response time distributions or response times for errors. Modeling speed-accuracy relationships has usually not been attempted.In this article, we show how the diffusion model (Ratcliff, 1978(Ratcliff, , 1981(Ratcliff, , 1985(Ratcliff, , 1988 Ratcliff, Van Zandt, & McKoon,...

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Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP (http://www.jasp-stats.org), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder’s BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.