Correlations are a popular analysis tool in psychology to examine the extent to which two variables are related.
Bayesian updating formula
Several pioneering initiatives have been introduced which, if embraced by the community, will leave psychological science in a strong position moving forward.
Here I focus on three I believe are the most important.
The distribution of interest for inference is now this new distribution pertaining to the partial correlation parameter.
Recall that the frequentist estimate of the partial correlation coefficient was .
The mode of this posterior distribution was 0.205, with a 95% Highest-Density Interval spanning from -0.03 to 0.39.
Note that whilst the modal estimate of the partial correlation parameter was close to that of the frequentist analysis, the Bayesian parameter estimation provides much more information, in particular regarding the uncertainty of this estimate.Another QRP could include analysing your data in a variety of ways (for example, maybe a couple of participants didn’t show the effect you were looking for, so why not remove them from the analysis and see whether that “clears things up”? What was concerning about this study is that many of these QRPs were not really considered “questionable” at the time.Indeed, many researchers have admitted to engaging in such QRPs (John et al., 2013).In order to do this, one needs to use partial correlations.Whilst there are relatively straightforward methods to calculate partial correlations using frequentist statistics, I was interested recently whether there is a Bayesian parameter estimation version of this analysis.The final article was, of course, edited down by their team to meet the 300 word guide. That there is a reproducibility crisis in psychological science—and arguably across all sciences—is, to me, beyond doubt.