Meta-analysis is crucial to coping with the contemporary landscape of exponential scientific output. Hindering this effort is effect size variety, with standardized beta coefficients, regression weights, elasticities, or partial correlations proven to be non-equivalent to zero-order correlations, despite that these parameters are often aggregated together. Addressing this challenge, we developed two novel approaches that convert betas to correlations, uninformed and informed estimation, and compare their accuracy and bias against the traditional method of Peterson and Brown (2005). In our simulations, we tested matrices from 3 to 10 variables, finding that Peterson and Brown’s technique is inherently biased, less accurate, and misestimates error variance. Uninformed and informed estimation was on average more accurate, unbiased and, by merging sampling error with imputation error, correctly identifies error variance. Due to imputation error, reporting beta weights alone typically destroys 95% to over 99% of the information originally held by a full correlation matrix. For fields that almost exclusively report betas, such as Economics, it necessarily cripples them from becoming cumulative sciences. We recommend that all previous uses of Peterson and Brown be re-evaluated, future aggregations of partial correlations should use our provided estimation techniques, and correlation matrices be routinely reported.
