Maximum likelihood difference scales represent perceptual magnitudes and predict appearance matches.

One central problem in perception research is to understand how internal experiences are linked to physical variables. Most commonly, this relationship is measured using the method of adjustment, but this has two shortcomings: The perceptual scales that relate physical and perceptual variables are not measured directly, and the method often requires perceptual comparisons between viewing conditions. To overcome these problems, we measured perceptual scales of surface lightness using maximum likelihood difference scaling, asking observers only to compare the lightness of surfaces presented in the same context. Observers were lightness constant, and the perceptual scales qualitatively and quantitatively predicted perceptual matches obtained in a conventional adjustment experiment. Additionally, we show that a contrast-based model of lightness perception predicted 98% of the variance in the scaling and 88% in the matching data. We suggest that the predictive power was higher for scales because they are closer to the true variables of interest.