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On the meta‐analysis of response ratios for studies with correlated and multi‐group designs
Author(s) -
Lajeunesse Marc J.
Publication year - 2011
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/11-0423.1
Subject(s) - statistics , meta analysis , sample size determination , metric (unit) , variance (accounting) , multivariate analysis of variance , multivariate statistics , analysis of variance , mathematics , random effects model , econometrics , ecology , computer science , biology , engineering , medicine , business , operations management , accounting
A common effect size metric used to quantify the outcome of experiments for ecological meta‐analysis is the response ratio (RR): the log proportional change in the means of a treatment and control group. Estimates of the variance of RR are also important for meta‐analysis because they serve as weights when effect sizes are averaged and compared. The variance of an effect size is typically a function of sampling error; however, it can also be influenced by study design. Here, I derive new variances and covariances for RR for several often‐encountered experimental designs: when the treatment and control means are correlated; when multiple treatments have a common control; when means are based on repeated measures; and when the study has a correlated factorial design, or is multivariate. These developments are useful for improving the quality of data extracted from studies for meta‐analysis and help address some of the common challenges meta‐analysts face when quantifying a diversity of experimental designs with the response ratio.