Maximum-likelihood procedures and the inattentive observer

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Abstract
In most experimental situations, it is expected that observers will achieve perfect detection at extremely high signal levels. Technically, it is assumed that the asymptote of the psychometric function is unity. In many practical psychophysical tests, such as those involving children, patients, or nonhuman animals, the observers are occasionally inattentive. Using computer simulations, it was assumed that inattention can be modeled as a stationary stochastic process whose major effect is to produce a psychometric function having an asymptote less than unity. A maximum-likelihood procedure was used to estimate threshold, because it has been shown to provide reasonably stable threshold estimates using very few observations. Inattention increases the variability of the threshold estimate, as would be expected, because inattention reduces the slope of the psychometric function. The simulations also show that the maximum-likelihood procedure poorly estimates the amount of inattention, and can, thereby, produce a strong bias in the threshold estimates, overestimating or underestimating the true values under different circumstances. Inattention appears to affect the two-alternative forced-choice procedure more strongly than the yes–no (go/nogo) procedure.

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