Classification images reveal decision variables and strategies in forced choice tasks

Despite decades of research, there is still uncertainty about how people make simple decisions about perceptual stimuli. Most theories assume that perceptual decisions are based on decision variables, which are internal variables that encode task-relevant information. However, decision variables are usually considered to be theoretical constructs that cannot be measured directly, and this often makes it difficult to test theories of perceptual decision making. Here we show how to measure decision variables on individual trials, and we use these measurements to test theories of perceptual decision making more directly than has previously been possible. We measure classification images, which are estimates of templates that observers use to extract information from stimuli. We then calculate the dot product of these classification images with the stimuli to estimate observers' decision variables. Finally, we reconstruct each observer's "decision space," a map that shows the probability of the observer's responses for all values of the decision variables. We use this method to examine decision strategies in two-alternative forced choice (2AFC) tasks, for which there are several competing models. In one experiment, the resulting decision spaces support the difference model, a classic theory of 2AFC decisions. In a second experiment, we find unexpected decision spaces that are not predicted by standard models of 2AFC decisions, and that suggest intrinsic uncertainty or soft thresholding. These experiments give new evidence regarding observers' strategies in 2AFC tasks, and they show how measuring decision variables can answer long-standing questions about perceptual decision making.