# [R-meta] quick question about covariances

Viechtbauer, Wolfgang (SP) wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Fri Nov 16 17:21:05 CET 2018

```See below for my responses.

Best,
Wolfgang

>-----Original Message-----
>From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-
>project.org] On Behalf Of Andrew Guerin
>Sent: Friday, 16 November, 2018 17:13
>To: r-sig-meta-analysis using r-project.org
>Subject: [R-meta] quick question about covariances
>
>Hi, I am running an analysis in which I need to generate a variance-
>covariance matrix for data with shared controls ('multiple treatments
>dependence').
>I have done this before with standardised mean differences, raw mean
>differences, and lnVR - calculating the covariances using formulas on the
>metafor website and graciously provided by James Pustejovsky.
>
>This time my effect size data are log mean ratios / response ratios, and
>I was hoping someone could check my logic.
>
>Given that the sampling variance for the effect size  - obtained using
>escalc(measure="ROM", vtype="LS"...) - seems to be based on the formula
>(from Hedges 1999)
>
>v = (sdc ^ 2  / (nc * mc ^ 2)) + (sde ^ 2  / (ne * me ^ 2))
>
>sdc, nc , mc  are sd, n and mean for the control treatment
>sde, ne, me are the same for the experimental samples
>
>then does it follow that the covariance for samples which share the same
>control will simply be
>
>Cov = sdc ^ 2  / (nc * mc ^ 2) ?

Correct.

>Out of curiosity, if I were to use vtype="HO" instead, where the formula
>for the sampling variance is
>
>v =  (sdp ^ 2)   *    (1  / (nc * mc ^ 2)) + (1  / (ne * me ^ 2))
>
>sdp = pooled standard deviation.
>
>Then presumably it is more complicated to calculate the covariance since
>sdp is already calculated using nc, sdc, ne, and sde, so would be
>different for every control-treatment pair.

Yes, this would complicate things.

```