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Julia M Haaf1, Jeffrey N Rouder1

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Bayesian mixed models reveal that most individuals exhibit the Stroop effect. However, some participants violate order restrictions in the Simon task, responding faster to incongruent stimuli.

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Area of Science:

  • Psychological science
  • Cognitive psychology
  • Bayesian statistics

Background:

  • Model comparison in Bayesian mixed models is increasingly utilized in psychological research.
  • Order restrictions across individuals in psychological tasks require specialized modeling approaches.

Purpose of the Study:

  • To develop and apply a Bayesian model-comparison strategy for assessing order restrictions across participants in psychological tasks.
  • To investigate whether effects consistently follow predicted orders (e.g., Stroop effect) or if individual-level violations occur.

Main Methods:

  • Development of nested Bayesian models to incorporate simultaneous order restrictions for numerous participants.
  • Utilizing Bayes factor model comparison with Zellner and Siow's default g-priors.
  • Application to seven datasets from Stroop, Simon, and Eriksen interference tasks.

Main Results:

  • Confirmation that all participants demonstrate the Stroop effect (congruent colors named faster than incongruent ones).
  • Discovery of violations in order constraints for some individuals in the Simon task, where spatially incongruent responses were faster than congruent ones.
  • Demonstration of the feasibility of Bayesian methods for handling complex order-restricted models intractable in frequentist approaches.

Conclusions:

  • Bayesian modeling effectively captures individual differences in response patterns, particularly order restrictions.
  • Task-specific differences in order constraint adherence (e.g., Stroop vs. Simon tasks) warrant further investigation.
  • The developed methodology provides a robust framework for analyzing order-restricted effects in psychological science.