Variance and covariance of ecological effect sizes that share a common control.

by Bryan MacNeill

Submitted : Spring 2016

Conventional effect sizes use treatment and control group outcomes to quantify the magnitude and direction of published study outcomes. An emerging problem with these effect sizes is that ecologists design experiments that compare a single control outcome with multiple treatment effects. This results in statistical dependencies among effect sizes from single studies. Here I will derive the correct covariances for multiple effect sizes that share a common control. Using data from Altshuler’s 2010 paper on hummingbird flight kinematics as an example, I will use the multivariate delta method to estimate covariances for the effect size metric: Hedges’ d. These covariances will be useful when modeling dependencies in ecological meta-analysis.

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