Both the speed and the accuracy of a perceptual judgment depend on the strength of the sensory stimulation. When stimulus strength is high, accuracy is high and response time is fast; when stimulus strength is low, accuracy is low and response time is slow. Although the psychometric function is well established as a tool for analyzing the relationship between accuracy and stimulus strength, the corresponding chronometric function for the relationship between response time and stimulus strength has not received as much consideration. In this article, we describe a theory of perceptual decision making based on a diffusion model. In it, a decision is based on the additive accumulation of sensory evidence over time to a bound. Combined with simple scaling assumptions, the proportional-rate and power-rate diffusion models predict simple analytic expressions for both the chronometric and psychometric functions. In a series of psychophysical experiments, we show that this theory accounts for response time and accuracy as a function of both stimulus strength and speed-accuracy instructions. In particular, the results demonstrate a close coupling between response time and accuracy. The theory is also shown to subsume the predictions of Piéron's Law, a power function dependence of response time on stimulus strength. The theory's analytic chronometric function allows one to extend theories of accuracy to response time.

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Most theories of visual search emphasize issues of limited versus unlimited capacity and serial versus parallel processing. In the present article, we suggest a broader framework based on two principles, one empirical and one theoretical. The empirical principle is to focus on conditions at the intersection of visual search and the simple detection and discrimination paradigms of spatial vision. Such simple search conditions avoid artifacts and phenomena specific to more complex stimuli and tasks. The theoretical principle is to focus on the distinction between high and low threshold theory. While high threshold theory is largely discredited for simple detection and discrimination, it persists in the search literature. Furthermore, a low threshold theory such as signal detection theory can account for some of the phenomena attributed to limited capacity or serial processing. In the body of this article, we compare the predictions of high threshold theory and three versions of signal detection theory to the observed effects of manipulating set size, discriminability, number of targets, response bias, external noise, and distractor heterogeneity. For almost all cases, the results are inconsistent with high threshold theory and are consistent with all three versions of signal detection theory. In the Discussion, these simple theories are generalized to a larger domain that includes search asymmetry, multidimensional judgements including conjunction search, response time, search with multiple eye fixations and more general stimulus conditions. We conclude that low threshold theories can account for simple visual search without invoking mechanisms such as limited capacity or serial processing.