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Updated: Jan 27, 2026

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
Published on: September 17, 2019
A psychometrics of individual differences in experimental tasks
Jeffrey N Rouder1, Julia M Haaf2
1University of California, Irvine, CA, USA. jrouder@uci.edu.
Aggregating task performance data can obscure true correlations between cognitive processes. New analysis methods reveal that Stroop and flanker task inhibition are likely unrelated, challenging unified inhibition theories.
Area of Science:
- Cognitive Psychology
- Individual Differences Research
- Psychometrics
Background:
- Researchers often correlate task performance to identify shared latent processes.
- Observed low correlations between tasks with presumed commonalities are a persistent challenge.
- This may stem from statistical artifacts (e.g., low individual variability) or substantive issues (e.g., inhibition not being a unified concept).
Purpose of the Study:
- To investigate whether low correlations in individual-differences research are due to statistical aggregation or genuine lack of shared processes.
- To propose and validate an alternative analysis method that accounts for trial-by-trial variability.
- To re-evaluate the relationship between Stroop and flanker task inhibition.
Main Methods:
- Proposed an analysis approach that incorporates trial-by-trial variability and inter-individual covariation.
- Utilized common hierarchical models for implementation.
- Applied the method to data from Hedge et al. (2018) comparing Stroop and flanker tasks.
Main Results:
- The proposed method rescues classical psychometric concepts like effect size, reliability, and correlation.
- Bayes-factor analysis provided strong support for a lack of correlation between the Stroop and flanker tasks.
- This indicates that inhibition measured by these tasks may not be a unified construct.
Conclusions:
- Trial-by-trial aggregation can significantly attenuate effect sizes and correlations in cognitive tasks.
- The findings challenge the notion of a unified inhibitory process, suggesting Stroop and flanker inhibition are distinct.
- This research offers a more accurate approach to studying individual differences in cognitive tasks.
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