Revisiting and expanding the meta-analysis of variation: The log coefficient of variation ratio, lnCVR

Abstract

Meta-analyses are frequently used to quantify the difference in the average values of two groups (e.g., control and experimental treatment groups), but examine the difference in the variability (variance) of two groups. For such comparisons, the two relatively new effect size statistics, namely the log-transformed variability ratio (the ratio of two standard deviations; lnVR) and the log-transformed CV ratio (the ratio of two coefficients of variation; lnCVR) are useful. In practice, lnCVR may be of most use because a treatment may affect the mean and the variance simultaneously. We review current, and propose new, estimators for lnCVR and lnVR. We also present methods for use when the two groups are dependent (e.g., for cross-over and pre-test-post-test designs). A simulation study evaluated the performance of these estimators and we make recommendations about which estimators one should use to minimise bias. We also present two worked examples that illustrate the importance of accounting for the dependence of the two groups. We found that the degree to which dependence is accounted for in the sampling variance estimates can impact heterogeneity parameters such as{tau} 2 (i.e., the between-study variance) and I2 (i.e., the proportion of the total variability due to between-study variance), and even the overall effect, and in turn qualitative interpretations. Meta-analytic comparison of the variability between two groups enables us to ask completely new questions and to gain fresh insights from existing datasets. We encourage researchers to take advantage of these convenient new effect size measures for the meta-analysis of variation.