Are most published research findings false in a continuous universe?

Abstract

Diagnostic screening models for the interpretation of null hypothesis significance test (NHST) results have been influential in highlighting the effect of selective publication on the reproducibility of the published literature, leading to John Ioannidis' much-cited claim that most published research findings are false. These models, however, are typically based on the assumption that hypotheses are dichotomously true or false, without considering that effect sizes for different hypotheses are not the same. To address this limitation, we develop a simulation model that overcomes this by modeling effect sizes explicitly using different continuous distributions, while retaining other aspects of previous models such as publication bias and the pursuit of statistical significance. Our results show that the combination of selective publication, bias, low statistical power and unlikely hypotheses consistently leads to high proportions of false positives, irrespective of the effect size distribution assumed. Using continuous effect sizes also allows us to evaluate the degree of effect size overestimation and prevalence of estimates with the wrong sign in the literature, showing that the same factors that drive false-positive results also lead to errors in estimating effect size direction and magnitude. Nevertheless, the relative influence of these factors on different metrics varies depending on the distribution assumed for effect sizes. The model is made available as an R ShinyApp interface, allowing one to explore features of the literature in various scenarios.