[Feature Request] `escalc` Convert Correlations to Cohen's D and Hedge's G?

[emstruong]

Hello,

Thank you for the great package.

I was wondering if it'd be possible for escalc to support converting correlations to Cohen's D? And perhaps Hedge's G, if possible?

Equation 11.80 of the Cooper et al. (2019, Handbook of Research Synthesis and Meta-Analysis, 3E) gives

$$ d = \frac{2r}{\sqrt{1-r^2}} $$

and

$$ v_d = \frac{4v_r}{(1-r^2)^3} $$

So I think the conversion to Cohen's D should be possible...

[emstruong]

I just realized that escalc seems to already support converting r to Hedge's G, but it may require that m1i, m2i, sd1i, sd2i, n1i, n2i be specified even though they don't seem particularly relevant for getting to Cohen's D and may be mostly empty for a particular effect size calculation.

At least for getting Cohen's D, only ni and ri should be needed...?

I'm not very familiar with this...

[wviechtb]

escalc() already supports the conversion of d-values to Hedges' g values:

escalc(measure="SMD", di=0.5, n1i=20, n2i=20)

The equations you are showing are for converting a point-biserial correlation coefficient to a d-value, assuming that the two groups are of equal size. This has nothing to do with converting d to g. But escalc() also provides that:

escalc(measure="SMD", ri=0.25, n1i=20, n2i=20)

(the bias-correction is also automatically applied here). Again, this only makes sense if the correlation is a point-biserial correlation (which is very rarely the case). If it is a regular Pearson product-moment correlation coefficient between two quantitative variables, then this conversion is not appropriate.

[emstruong]

Thank you for informing me about this issue.

I'm surprised that neither Section 11.6.3 nor Figure 11.2 of the handbook raise the assumption of the point-biserial correlation coefficient.

Would you happen to know of a reference that I could read to know more about this issue or perhaps effect computation/conversion?

[wviechtb]

You could take a look at this article:

Jacobs, P., & Viechtbauer, W. (2017). Estimation of the biserial correlation and its sampling variance for use in meta-analysis. Research Synthesis Methods, 8(2), 161-180. https://doi.org/10.1002/jrsm.1218