I am conducting a meta-analysis using raw mean scores as effect sizes (i.e., reported test scores on a certain standardized test).
I found a calculation formula for sampling variances provided by, e.g., Card (2012, p. 150), Hox (2010, p. 209), and also [Calculation for the estimated sampling variance of individual group raw mean.
SEx = Sx/√N
sis the standard deviation of variable
Nis the sample size.
Especially, Card's book,
Applied Meta-analysis for social science research was very helpful providing an equation for transforming scores between two different scales.
Card (2012, p. 148)
X2 = ((X1 - Min1)((Max2 - Min2)/(Max1 - Min1))+Min2
- where, X2 is the equivalent score on the second scale
- X1 is the score on the first scale that you wish to transform.
- Min1 is the lowest possible score on the first scale.
- Max1 is the highest possible score on the first scale.
- Min2 is the lowest possible score on the second scale.
- Max2 is the highest possible score on the second scale.
However, the book does not provide how to calculate sampling variances when ESs were transformed into a standardized value.
I would really appreciate it if you could let me know how sampling variances could be calculated for this standardized effect size. If possible, references that I can cite would be much appreciated.