# [R-meta] formula for calculating variance

Viechtbauer, Wolfgang (NP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Thu Dec 15 19:44:58 CET 2022

```Dear Sicong,

No, this would not be correct, because that equation for the sampling variance of d assumes that one has means and SDs available for the two groups. The proper way to compute the sampling variance of d when it was obtained by converting the log odds ratio to d involves applying the appropriate transformation to the variance of the log odds ratio. For example, one commonly used method for converting a log odds ratio to d is:

d = sqrt(3) / pi * logOR.

Then the variance of d is given by:

var(d) = 3 / pi^2 * var(logOR),

where var(logOR) is typically estimated as you point out with 1/A + 1/B + 1/C + 1/D.

PS: When posting to this mailing list with a new topic, don't just reply to a previous message and change the subject. The reply message still contains information about the original thread. When you do this, the threading in the archives is messed up. See:

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On
>Behalf Of Sicong Liu
>Sent: Thursday, 15 December, 2022 18:06
>Cc: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] formula for calculating variance
>
>Dear All,
>
>Hope all of you are doing well.
>
>I have a question regarding the calculation of the effect size variance on
>OddsRatio metric and wish to hear your thoughts:
>
>When computing the effect size variance based on odds ratio using binary data
>(assuming the four cells has observation number A, B, C, D like the example in
>Chapter 5 of Borenstein et al. (2009) book, p. 33), the formula suggested for
>calculating effect size variance is: var = 1/A + 1/B + 1/C + 1/D. My question is
>that if I convert the effect size from logOddsRatio to d, is it appropriate to
>calculate the effect size variance using the converted d in that: var = (n1 +
>n2)/(n1*n2) + d^2/(2*n1 + 2*n2) (Chapter 4, p. 27)? Regardless of the
>appropriateness, could you please explain the main differences between these two
>approaches in calculating effect size variances and how the selection between
>them may affect the modeling?
>
>Thank you very much and stay warm!
>
>Cheers,
>Sicong

```