Localizing Structure in Individual Differences: A Visual Illusion Case Study

Are people who are susceptible to one illusion susceptible to others? Previous research has shown small correlations, but might small values reflect attenuation from measurement error from trial-to-trial variation? To assess measurement error, we develop a set of novel data visualizations and hierarchical models. Data from 149 participants on 2 variants of 5 illusions were collected using an adjustment paradigm. The results showed low trial-noise and strong between-subject variability (e.g., signal-to-noise ratio $\approx 1.14$, reliability $\approx 0.93$). Correlations across illusions are low, around $0.22 \pm 0.07$. A Bayesian hierarchical analysis reveals minimal attenuation from measurement error in these values. Though correlations are low, latent variable analysis reveals a common latent factor that loads on all tasks and explains about 23.3\% of the variance in illusion susceptibility.