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