Footprint of publication selection bias on meta-analyses in medicine, environmental sciences, psychology, and economics.

Publication selection bias undermines the systematic accumulation of evidence. To assess the extent of this problem, we survey over 68,000 meta-analyses containing over 700,000 effect size estimates from medicine (67,386/597,699), environmental sciences (199/12,707), psychology (605/23,563), and economics (327/91,421). Our results indicate that meta-analyses in economics are the most severely contaminated by publication selection bias, closely followed by meta-analyses in environmental sciences and psychology, whereas meta-analyses in medicine are contaminated the least. After adjusting for publication selection bias, the median probability of the presence of an effect decreased from 99.9% to 29.7% in economics, from 98.9% to 55.7% in psychology, from 99.8% to 70.7% in environmental sciences, and from 38.0% to 29.7% in medicine. The median absolute effect sizes (in terms of standardized mean differences) decreased from d = 0.20 to d = 0.07 in economics, from d = 0.37 to d = 0.26 in psychology, from d = 0.62 to d = 0.43 in environmental sciences, and from d = 0.24 to d = 0.13 in medicine.

Estimating the extent of selective reporting: An application to economics.

Using a sample of 70,399 published p-values from 192 meta-analyses, we empirically estimate the counterfactual distribution of p-values in the absence of any biases. Comparing observed p-values with counterfactually expected p-values allows us to estimate how many p-values are published as being statistically significant when they should have been published as non-significant. We estimate the extent of selectively reported p-values to range between 57.7% and 71.9% of the significant p-values. The counterfactual p-value distribution also allows us to assess shifts of p-values along the entire distribution of published p-values, revealing that particularly very small p-values (p < 0.001) are unexpectedly abundant in the published literature. Subsample analysis suggests that the extent of selective reporting is reduced in research fields that use experimental designs, analyze microeconomics research questions, and have at least some adequately powered studies.

p-Curve and p-Hacking in Observational Research.

The p-curve, the distribution of statistically significant p-values of published studies, has been used to make inferences on the proportion of true effects and on the presence of p-hacking in the published literature. We analyze the p-curve for observational research in the presence of p-hacking. We show by means of simulations that even with minimal omitted-variable bias (e.g., unaccounted confounding) p-curves based on true effects and p-curves based on null-effects with p-hacking cannot be reliably distinguished. We also demonstrate this problem using as practical example the evaluation of the effect of malaria prevalence on economic growth between 1960 and 1996. These findings call recent studies into question that use the p-curve to infer that most published research findings are based on true effects in the medical literature and in a wide range of disciplines. p-values in observational research may need to be empirically calibrated to be interpretable with respect to the commonly used significance threshold of 0.05. Violations of randomization in experimental studies may also result in situations where the use of p-curves is similarly unreliable.