We propose and demonstrate the shifted Wald (SW) distribution as both a useful measurement tool and intraindividual process model for psychological response time (RT) data. Furthermore, we develop a methodology and fitting approach that readers can easily access. As a measurement tool, the SW provides a detailed quantification of the RT data that is more sophisticated than mean and SD comparisons. As an intraindividual process model, the SW provides a cognitive model for the response process in terms of signal accumulation and the threshold needed to respond. The details and importance of both of these features are developed, and we show how the approach can be easily generalized to a variety of experimental domains. The versatility and usefulness of the approach is demonstrated on 3 published data sets, each with a different canonical mode of responding: manual, vocal, and oculomotor modes. In addition, model-fitting code is included with the article.