Why many studies of individual differences with inhibition tasks may not localize correlations.

Individual difference exploration of cognitive domains is predicated on being able to ascertain how well performance on tasks covary. Yet, establishing correlations among common inhibition tasks such as Stroop or flanker tasks has proven quite difficult. It remains unclear whether this difficulty occurs because there truly is a lack of correlation or whether analytic techniques to localize correlations perform poorly real-world contexts because of excessive measurement error from trial noise. In this paper, we explore how well correlations may localized in large data sets with many people, tasks, and replicate trials. Using hierarchical models to separate trial noise from true individual variability, we show that trial noise in 24 extant tasks is about 8 times greater than individual variability. This degree of trial noise results in massive attenuation in correlations and instability in Spearman corrections. We then develop hierarchical models that account for variation across trials, variation across individuals, and covariation across individuals and tasks. These hierarchical models also perform poorly in localizing correlations. The advantage of these models is not in estimation efficiency, but in providing a sense of uncertainty so that researchers are less likely to misinterpret variability in their data. We discuss possible improvements to study designs to help localize correlations.