[R-meta] Calculating variances and z transformation for tetrachoric, biserial correlations?

[Lists at dewey.myzen.co.uk]

Mark White <markhwhiteii at gmail.com> wrote :

Dear Mark

Can you resend in plain text? Your use of HTML means your e-mail was scrambled by the time it reached here.

> Hello,
> 
> I have converted a number of summary statistics (contingency tables, *t-*
> and
> *F*-statistics,* M*s and *SD*s) to tetrachoric and biserial correlations.
> The other effect sizes that I directly observed were raw correlations. I
> have my model all set up to run, but I am unsure as to what to do about
> these effect sizes. I see two options:
> 
> 1. Submit raw, tetrachoric, and biserial correlations and their variances
> to analyses directly (what I have now).
> 
> 2. Do Fisher's r-to-z transformation and *then *submit those to analyses.
> The problem here is: How do I convert tetrachoric and biserial correlations
> to Fisher's z? And if I do that, can I just use N to calculate the
> variance? Or, do I have to also convert the variances of tetrachoric and
> biserial correlations?
> 
> In either case, I am not sure how `metafor::escalc` calculates variances
> for tetrachoric (`RTET`) and biserial (`RBIS`) correlations. I tried
> looking through the code for `metafor::escalc` on GitHub, but could not
> figure out the calculations.
> 
> I have included a table describing my effect sizes and how I calculated
> them/their variances below.
> 
> What do you all think would be the best way to handle these data?
> 
> *Effect size*
> 
> *k*
> 
> *Effect size calculation*
> 
> *Variance calculation*
> 
> Raw correlation
> 
> 217
> 
> Directly observed
> 
> Typical large-samples estimation (see Hedges, 1989, Equation 5), using
> `metafor::escalc`
> 
> Tetrachoric correlation
> 
> 12
> 
> From 2 x 2 contingency tables, using `metafor::escalc`
> 
> From 2 x 2 contingency tables, using `metafor::escalc`
> 
> 
> *Unsure what the formula is*
> 
> Biserial correlation (from *t*- or *F*-statistic)
> 
> 8
> 
> From *t*- or *F*-statistic to point-biserial correlation (using
> `compute.es::tes`
> and `compute.es::fes`) to biserial correlation (self-written function based
> on Jacobs & Viechtbauer, 2016, assuming *n*s equal across conditions)
> 
> From *n*, using self-written function based on Soper's method (Jacobs &
> Viechtbauer, 2016, Equation 13, assuming *n*s equal across conditions)
> 
> Biserial correlation (from *M *and *SD*)
> 
> 2
> 
> From means and standard deviations directly, using `metafor::escalc`
> 
> From means and standard deviations directly, using `metafor::escalc`
> 
> 
> *Unsure what the formula is*
> 
> Square-root of eta-squared
> 
> 1
> 
> F-statistic to Cohen’s *f*  (Cohen, 1988) to eta-squared to square-root of
> eta-squared as an approximation of a raw correlation coefficient (Lakens,
> 2013), using self-written function
> 
> 
> 
> *This was a one-way ANOVA with three means (low, medium, high prejudice).*
> 
> Typical large-samples estimation (see Hedges, 1989, Equation 5), using
> `metafor::escalc`
> 
> Best,
> Mark
> 
> 	[[alternative HTML version deleted]]
> 
> _______________________________________________
> R-sig-meta-analysis mailing list
> R-sig-meta-analysis at r-project.org
> https://stat.ethz.ch/mailman/listinfo/r-sig-meta-analysis