My question concerns the calculation of effect size variance for studies that are going to be included in a meta-analysis. I want to calculate variance so that I can weight each study by the inverse of it's variance in a meta-regression.
It is established that you need to calculate variance in different ways when you have different study designs. For example, it must be calculated differently when you have completely randomised and matched study designs. (Matched means systematically paired or randomised block designs, for example). In a completely randomised design, you will use sample sizes, standard deviations and means of each treatment group to calculate the variance of the effect size. In matched designs, however, you are interested in the differences between each matched pair, and the number of pairs.
Borenstein et al. (2009) tell you how to calculate variance differently for Hedge's d and g for both randomised and matched designs, but does not tell you how to calculate variance for matched designs for log response ratio effect size.
I am doing a meta-analysis investigating differences in the number of species found in control and treatment types of forest. I am using the log response ratio (lnR) to represent proportional differences in the number of species between control and treatment forests. I have studies with both randomised and matched study designs.
So my question: How do you calculate the effect size variance for the log response ratio, for studies with randomised and matched study designs. What are the different calculations?