Unifying Different Psychometric Methods : Theory and Experiment

To estimate the sensitivity to discriminate two visual stimuli, the two-alternative forced choice (2AFC) paradigm has become a favorite method. The psychometric function that links the physical stimuli to discrimination performance can then be modeled using signal detection theory (SDT). Recent efforts to combine SDT with Bayesian probabilities have linked thresholds and biases to hypothesized prior knowledge and optimal encoding/decoding. When supra-thresholds are considered, the maximum likelihood difference scaling (MLDS) paradigm is a preferred method to estimate the perceptual scale that links a physical property to a psychological dimension. This latter method relies on the comparison of perceived differences between pairs of stimuli. Here, we are interested in modeling the MLDS paradigm with the Bayesian framework. This allows us to compare sensitivity measurements obtained from MLDS and 2AFC methods. We first show how the perceptual scale can be derived from SDT and Bayesian probabilities, thereby providing a unifying theoretical framework. In particular, we show that this theory predicts that the slope of the psychometric function at the point of subjective equality is proportional to the derivative of the perceptual scale. In other words, the perceptual scale is the scale that uniformizes the sensitivity. Next, we demonstrate the consistency of both experimental techniques and their compatibility with information theory (optimal coding) using human participants’ data. More precisely, we illustrate our theoretical results with two behavioral experiments: (i) new measurements of the perceptual scale of orientation and the sensitivity to discriminate nearby orientations, and (ii) previous measurements of the perceptual scale of interpolation between pairs of textures. Our results are important for future developments in psychophysics, both theoretically and experimentally. In particular, they support the use of the MLDS technique as a possible alternative to 2AFC for measuring psychophysical sensitivities.