 In many disciplines (e.g., psychology, psychiatry, materials science, pharmacology and toxicology, clinical medicine, biology and biochemistry, economics and business, microbiology and genetics) the proportion of statistically significant results is very high, close to or exceeding 90% (Fanelli 2010a). This is despite the fact that in many of these fields, the average statistical power is low—that is, the average probability that a study will correctly reject the null hypothesis is low. For example, in psychology the proportion of published results that are statistically significant is 92% despite the fact that the average power of studies in this field to detect medium effect sizes (arguably typical of the discipline) is roughly 44% (Szucs &amp; Ioannidis 2017). If there was no bias towards publishing statistically significant results, the proportion of significant results should roughly match the average statistical power of the discipline. The excess in statistical significance (in this case, the difference between 92% and 44%) is therefore an indicator the strength of the bias. For a second example, in ecology, environment and plant and animal sciences the proportion of statistically significant results is 74% and 78% respectively, admittedly lower than in psychology. However, the most recent estimate of the statistical power, again of medium effect sizes, of ecology and animal behaviour is 23–26% (Smith, Hardy, &amp; Gammell 2011) (An earlier more optimistic assessment was 40–47%, Jennions &amp; Møller, 2003.) For a third example, the proportion of statistically significant results in neuroscience and behaviour is 85%. Our best estimate of the statistical power in neuroscience is at best 31%, with a lower bound estimate of 8% (Button et al. 2013). The associated file-drawer problem (Rosenthal 1979)—where researchers relegate failed statistically non-significant studies to their file drawers, hidden from public view—has long been established in psychology and others disciplines, and is known to lead to distortions in meta-analysis (where a “meta-analysis” is a study which analyses results across multiple other studies).