The meta-analysis of response ratios in experimental ecology

Meta-analysis provides formal statistical techniques for summarizing the re sults of independent experiments and is increasingly being used in ecology. The response ratio (the ratio of mean outcome in the experimental group to that in the control group) and closely related measures of proportionate c hange are often used as measures of effect magnitude in ecology. Using thes e metrics for meta-analysis requires knowledge of their statistical propert ies, but these have not been previously derived. We give the approximate sa mpling distribution of the log response ratio, discuss why it is a particul arly useful metric for many applications in ecology, and demonstrate how to use it in meta-analysis. The meta-analysis of response-ratio data is illus trated using experimental data on the effects of increased atmospheric CO2 on plant biomass responses.