Hello,
I recently started using the metafor package (version 1.6-0) in R (2.15.1,
64-bit Windows 7) and noticed that I was getting slightly different values
when I manually calculated the standardized mean difference versus what
escalc was giving me. Here's a very simple example:
escalc(measure="SMD", m1i=5,m2i=10,n1i=5,n2i=5,sd1i=1,sd2i=2,vtype="LS")
The result is:
yi vi
1 -2.854599 0.8074367
However, if I calculate this manually using the pooled standard deviation
formula given in Cooper et al (2009)*, I get an SMD of -2.85625 and a
variance of 0.870205.
The formula given in Cooper et al for the pooled standard deviation is:
Swithin = sqrt(((n1i - 1) * Sd1i^2 + (n2i - 1) * Sd2i^2)/(n1i + n2i -2))
[1.581139 for my example]
And the formula for variance is:
Vd = (n1i + n2i)/(n1i*n2i) + d^2/(2 *(n1i+n2i)) [1.066667 for my example]
Where d is:
d = (m1i - m2i)/Swithin [-3.16228 for my example]
These are both corrected by the correction factor J:
J = 1 - 3/(4*(n1i+n2i-2)-1) [0.903226 for my example]
The resulting g is [0.903226 * -3.16228] = -2.85625 and the resulting
variance is [0.903226^2 * 1.06667] = 0.870205. Thus, my calculated SMD is
very close to the escalc value (only 0.05% different), but the variance is
nearly 8% different.
I assume the difference must lie in how the pooled standard deviation is
being calculated, but the help for escalc only says that the pooled standard
deviation is "calculated inside the function", and I can't find the exact
formula for how this is being done. I'm trying to track down a copy of
Hedges and Olkin (1985), but it would be great in the meantime somebody
could enlighten me.
Thanks,
Stephen Ban
*p. 226. Cooper, H., Hedges, L., and Valentine, J. The handbook of research
synthesis and metaanalysis. Russell Sage Foundation, 2009.
Stephen Ban, M.Sc.
Ph.D. Candidate
Australian Research Council Centre of Excellence for Coral Reef Studies
James Cook University
Townsville, Queensland 4811 Australia
Phone: +61 7 4781 6063
Fax: +61 7 4781 6722
<mailto:stephen....@jcu.edu.au> stephen....@my.jcu.edu.au
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