Estimating statistical power, posterior probability and publication bias of psychological research using the observed replication rate

In this paper, we show how Bayes' theorem can be used to better understand the implications of the 36% reproducibility rate of published psychological findings reported by the Open Science Collaboration. We demonstrate a method to assess publication bias and show that the observed reproducibility rate was not consistent with an unbiased literature. We estimate a plausible range for the prior probability of this body of research, suggesting expected statistical power in the original studies of 48–75%, producing (positive) findings that were expected to be true 41–62% of the time. Publication bias was large, assuming a literature with 90% positive findings, indicating that negative evidence was expected to have been observed 55–98 times before one negative result was published. These findings imply that even when studied associations are truly NULL, we expect the literature to be dominated by statistically significant findings.