Bias and correction for the log response ratio in ecological meta-analysis

Ecologists widely use the log response ratio for summarizing the outcomes of studies for meta-analysis. However, little is known about the sampling distribution of this effect size estimator. Here I show with a Monte Carlo simulation that the log response ratio is biased when quantifying the outcome of studies with small sample sizes, and can yield erroneous variance estimates when the scale of study parameters are near zero. Given these challenges, I derive and compare two new estimators that help correct this small-sample bias, and update guidelines and diagnostics for assessing when the response ratio is appropriate for ecological meta-analysis. These new bias-corrected estimators retain much of the original utility of the response ratio and are aimed to improve the quality and reliability of inferences with effect sizes based on the log ratio of two means.