Abstract In modern psychological science, many researchers use psychophysical tasks to study individual differences in perception, attention, aging, and personality. Psychophysics, however, traditionally uses designs with a great many trials and few individuals. These designs are inappropriate for individual-difference studies. Here, we develop a random-intercept psychophysics that jointly models variation across trials and individuals within a Bayesian hierarchical framework. We show that the model is ideal for measuring thresholds in small-trial designs. Because the model jointly accounts for variation across trials and individuals, it provides an assessment of correlation across tasks without the pernicious attenuation caused by trial noise. The resulting correlations are accompanied by measures of uncertainty that reflect both the number of trials per individual and the number of individuals. Because the framework is Bayesian, it is flexible, and we leverage this flexibility in two ways: First, we place factor models on the thresholds themselves, demonstrating how the structure of individual differences across a battery of tasks may be assessed. Second, we develop a custom-tailored psychophysical model for assessing whether stimulation is subliminal or superliminal. The threshold divides at chance-performance form above-chance performance, and the approach serves as a principled approach for assessing truly subliminal priming.
Rouder et al. (Mon,) studied this question.