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Two Bayesian corrections for attenuation in correlation analysis to investigate unconscious mental processes

Dr. Simone Malejka
University College London ~ Department of Experimental Psychology
Miguel A. Vadillo
Universidad Autónoma de Madrid, Spain
Zoltán Dienes
University of Sussex, United Kingdom
David R. Shanks
University College London, United Kingdom

As a method to investigate the scope of unconscious mental processes, researchers frequently obtain concurrent measures of implicit task performance and explicit stimulus awareness across participants. Even though both measures might be significantly greater than zero, the correlation between them might not, encouraging the inference that an unconscious process drives task performance. We highlight the pitfalls of this null-correlation approach with reference to a recent study by Salvador, Berkovitch, Vinckier, Cohen, Naccache, Dehaene, and Gaillard (2018), who reported a non-significant correlation between the extent to which memory was suppressed by a Think/No-Think cue and an index of cue awareness. First, in the Null Hypothesis Significance Testing (NHST) framework, it is inappropriate to interpret failure to reject the null hypothesis (i.e., correlation = 0) as evidence for the null. Instead, a Bayesian approach is needed to compare the support of the data for the null versus the alternative (i.e., correlation > 0) hypothesis. Second, the often low reliabilities of the performance and awareness measures can attenuate the correlation, making a positive correlation appear to be zero. Hence, the correlation must be inferred in a way that disattenuates the weakening effect of measurement (trial) error. We apply two Bayesian models that account for measurement error to the Salvador et al. data. The results provide at best anecdotal support for the claimed unconscious nature of participants’ memory-suppression performance. Researchers are urged to employ Bayesian methods that account for measurement error to analyze correlational data involving measures of performance and awareness rather than NHST methods.



Bayes factor
correlation analysis
measurement error
unconscious cognition


Bayesian Modeling
Hypothesis Testing
Measurement Theory

An extraordinary presentation. Thank you very much. I find it extremely useful to provide an introduction to Bayesian modeling. In the courses where we traditionally teach NHST, your contribution is very relevant to illustrate two fundamental aspects that you comment on: the importance of data and the importance of knowing how to correctly interpre...

Dr. Alfonso Díaz Furlong 2 comments

I believe for Model C, you fit the rate difference and SDT models, pull a point estimate and point uncertainty from each, and then use those values as input to the correlation model with parameter uncertainty. Have you considered going one step further, to include a Model D perhaps, where you implement all three models simultaneously, as component...

Dr. Beth Baribault 1 comment