Data Analysis and Power Simulations with General Linear Mixed Modelling for Psychophysical Data – A Practical, R-Based Guide

Abstract

Sample size planning is not straight-forward for the complex designs that are usually employed in psychophysical (two-alternative forced-choice) experiments: characteristics such as binary response variables and nested data structures where responses may be correlated differently within participants and experimental sessions than across participants and experimental sessions make it harder to estimate the necessary number of participants and trials with traditional means. In this practical R-based guide, we first show in detail how we can simulate verisimilar psychophysical data. We then use these simulations to compare two different methods by which two-alternative forced-choice data can be analyzed: (1) the “two-step” approach, where first psychometric functions are fitted and then statistical tests are performed over the parameters of these fitted psychometric functions; (2) an approach based on Generalized Linear Mixed Modeling (GLMM) that does not require the intermediary step of fitting psychometric functions. We argue that the GLMM approach enhances statistical validity and show that it can increase statistical power. Finally, we provide a sample implementation of a simulation-based power analysis that can be used as-is for many simple designs, but is also easily adaptable for more complex designs. Overall, we show that a GLMM-based approach can be beneficial for data analysis and sample size planning for typical (two-alternative forced-choice) psychophysical designs.