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Ingo Fründ, N. Valentin Haenel, Felix A. Wichmann; Estimating psychometric functions in nonstationary observers. Journal of Vision 2010;10(7):1135. doi: 10.1167/10.7.1135.
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© ARVO (1962-2015); The Authors (2016-present)
The psychometric function relates a physical dimension, such as stimulus contrast, to the responses of an observer. This relation is conveniently summarized by fitting a parametric model to the responses. In fitting such a model, we typically assume the responses to be independent of each others, and to follow the same distribution if recorded at the same stimulus level. However, there is evidence that casts doubt on the validity of this independence assumption: responses in psychophysical tasks are mutually dependent due to factors such as learning, fatigue, or fluctuating motivation. These kinds of dependencies are summarized as nonstationary behavior. From a theoretical point of view, nonstationarity renders inference about psychometric functions incorrect–it can result in rejection of otherwise correct psychometric functions or wrong credible intervals for thresholds and other characteristics of the psychometric function. So far, it is unknown how severe these errors are and how to properly correct for them. We simulated a number of observers with different types of nonstationary behavior. Psychometric functions were fitted for a large number of experimental settings, defined by the number of trials, the number of experimental blocks, and the task (2AFC vs yes-no). We present criteria to identify psychometric functions that are influenced by nonstationarity. Furthermore, we develop strategies that can be applied in different statistical paradigms–frequentist and Bayesian–to correct for errors introduced by nonstationary behavior. A software that automates the proposed procedures will be made available.
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