In the perceptual sciences, experimenters study the causal mechanisms of perceptual systems by probing observers with carefully constructed stimuli. It has long been known, however, that perceptual decisions are not only determined by the stimulus, but also by internal factors. Internal factors could lead to a statistical influence of previous stimuli and responses on the current trial, resulting in serial dependencies, which complicate the causal inference between stimulus and response. However, the majority of studies do not take serial dependencies into account, and it has been unclear how strongly they influence perceptual decisions. We hypothesize that one reason for this neglect is that there has been no reliable tool to quantify them and to correct for their effects. Here we develop a statistical method to detect, estimate, and correct for serial dependencies in behavioral data. We show that even trained psychophysical observers suffer from strong history dependence. A substantial fraction of the decision variance on difficult stimuli was independent of the stimulus but dependent on experimental history.We discuss the strong dependence of perceptual decisions on internal factors and its implications for correct data interpretation.

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Measuring sensitivity is at the heart of psychophysics. Often, sensitivity is derived from estimates of the psychometric function. This function relates response probability to stimulus intensity. In estimating these response probabilities, most studies assume stationary observers: Responses are expected to be dependent only on the intensity of a presented stimulus and not on other factors such as stimulus sequence, duration of the experiment, or the responses on previous trials. Unfortunately, a number of factors such as learning, fatigue, or fluctuations in attention and motivation will typically result in violations of this assumption. The severity of these violations is yet unknown. We use Monte Carlo simulations to show that violations of these assumptions can result in underestimation of confidence intervals for parameters of the psychometric function. Even worse, collecting more trials does not eliminate this misestimation of confidence intervals. We present a simple adjustment of the confidence intervals that corrects for the underestimation almost independently of the number of trials and the particular type of violation.