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Updated: Jul 16, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
Published on: September 17, 2019
Some do and some don't? Accounting for variability of individual difference structures.
Julia M Haaf1, Jeffrey N Rouder2,3
1University of Missouri, Columbia, MO, USA. jhaaf@mail.missouri.edu.
This study introduces Bayesian models to analyze individual differences in cognitive tasks like the Stroop task. Findings suggest most individuals exhibit consistent effects, challenging the idea of widespread negative or null effects in standard tasks.
Area of Science:
- Cognitive Psychology
- Psychometrics
- Bayesian Modeling
Background:
- Traditional view: Individual performance in cognitive tasks varies continuously.
- Stroop task example: Assumed average effect with a standard deviation, allowing for positive, smaller, or even negative effects.
- Uncertainty: Whether truly negative or null effects exist in tasks like Stroop.
Purpose of the Study:
- Develop models to investigate the presence of negative, null, and positive effects across individuals in cognitive tasks.
- Determine if all individuals exhibit positive effects or if some show no effect or negative effects.
- Apply these models to Stroop interference and priming experiments.
Main Methods:
- Development of a family of Bayesian hierarchical models.
- Models designed to capture various constraints on effect types (positive, null, negative).
- Application to Stroop interference and near-liminal priming experiments.
Main Results:
- Most individuals display similar effects within a given task; for instance, universal positive Stroop effects.
- Evidence suggests that negative or null Stroop effects are rare or non-existent in typical experimental settings.
- Demonstration that under specific conditions, individuals can be induced to exhibit null Stroop effects.
Conclusions:
- Bayesian hierarchical models provide a robust framework for analyzing individual differences in cognitive effects.
- Empirical evidence largely supports homogeneity in cognitive task performance, with positive effects being predominant.
- The existence of truly negative or null effects is task- and condition-dependent, not a general phenomenon.
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