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
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