# [R] {metafor} variance explaination for paired pre-test/posttest

John Williams johnwilliams at fas.harvard.edu
Tue Apr 8 02:29:59 CEST 2014

```In a previous post
https://stat.ethz.ch/pipermail/r-help/2012-April/308946.html
<https://stat.ethz.ch/pipermail/r-help/2012-April/308946.html>  , the
following calculation was given for imputing the variance of change scores
for paired studies:

// begin quote

2) Often, the dependent variable is not the same in each study. Then you
will have to resort to a standardized outcome measure. There are two
options:

a) standardization based on the change score standard deviation

Then yi = (m1i - m2i) / sdi with sampling variance vi = 1/ni + yi^2 /
(2*ni).

// end quote

I used the sampling variance equation above in a paper that is being
reviewed by a coauthor, who is a biostatistician.

He commented that he has never seen this equation for variance before, and
it looks strange to him. To put my knowledge into perspective, I am an
undergraduate taking my first statistics course. I imputed the t-statistic
from two-sided p-values reported in the paper, and used that to get the sdi
(as in the previous post).

I consulted the Cochrane Handbook and The Handbook of Research Syntheses and
Meta-analysis 2nd Ed (Cooper, Hedges, Valentine 2009) and couldn't find that
equation anywhere.

Would Prof. Viechtbauer, or anyone else knowledgeable, mind explaining the
sample variance above? I need to be able to defend my choice of equation.
Since it's the only method that I found that doesn't rely on a correlation
coefficient (which are not included in the papers), I'd like to be able to
justify it and not redo calculations for 23 studies if possible.

Thank you very much,

John

~~~~
John Williams
ALB Candidate, Harvard University (Expected May 2014)
johnwilliams at fas.harvard.edu
jawilliamsjr at gmail.com

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