A robust and readily implementable method for the meta-analysis of response ratios with and without missing standard deviations

The log response ratio, lnRR, is the most frequently used effect size statistic in ecology. However, missing standard deviations (SDs) are often present in meta-analytic datasets, preventing us from obtaining the sampling variance for lnRR. We propose three new methods to deal with missing SDs. All three methods use the square of the weighted average coefficient of variation CV to obtain sampling variances for lnRR when SDs are missing. Using simulation, we find that using the average CV to estimate the sampling variances for all observations, regardless of missingness, performs best. Surprisingly, even where SDs are missing, this simple method performs better than the conventional analysis with no missing SDs. This is because the conventional method incorporates biased estimates of sampling variances as opposed to less biased sampling variances with the average CV. All future meta-analyses of lnRR could take advantage of our new approach along with the other methods.