A simple formula for Bayesian shrinkage to correct regression to the mean
Wed-HS1-Talk VII-04
Presented by: Simone Malejka
As a method to investigate the scope of unconscious mental processes, researchers frequently collect a behavioral measure (e.g., some assessment of learning) and a measure of awareness (e.g., recognition judgments) of the critical cue or contingency. Evidence that behavioral change was indeed unconscious may require that participants were unaware of the critical regularity or that behavior and awareness are independent—both of which are commonly demonstrated using standard statistical tests (e.g., t-tests, correlation/regression analysis). We highlight a critical limitation in these approaches: Systematic bias caused by ignored measurement error (e.g., regression to the mean, regression attenuation) can lead to false-positive rates up to 100%. As a solution, we propose a correction formula for observed data based on the ideas of true-score estimation in educational testing and shrinking estimates towards a grand mean in Bayesian modeling. Because error is defined as imprecise measurement of an individual’s true score, information about the individual (e.g., their group membership) and the measure (e.g., its reliability) can be used to move observed scores closer to their true scores. Our formula provides corrected estimates as a weighted combination of the observed score and the group mean. We discuss different weighting methods and compare their performances in simulation studies. Our work shows that true-score estimation provides the means to correct data for measurement error: The corrected data offer a more representative sample to test the research hypothesis and consequently better inferences in scientific decision-making. We conclude by offering best practices for correcting measurement error in psychological research.
Keywords: unconscious processes, implicit cognition, measurement error, reliability, regression to the mean, Bayesian methods