Add additional logOR to d transofmration

[mattansb]

$$ d_{Cox} = \ln(OR) / 1.65 $$

Also note that since these are linear transformations, the SE of the resulting d is the transformed SE of the log(OR).

[bwiernik]

Where does the 1.65 come from? The standard reference for this approximate conversion is https://DOI.org/10.1002/1097-0258(20001130)19:22<3127::AID-SIM784>3.0.CO;2-M

There, based on the SD of the standard logistic distribution, it would be divide by (pi / sqrt(3)), which is approximately 1.813

[mattansb]

We already have the 3/sqrt(pi) conversion. 1.65 is from Sánchez-Meca, et al. (2003). Effect-size indices for dichotomized outcomes in meta-analysis. Psychological methods, 8(4), 448 (citing Cox 1970).

A user (meta-analyst) emailed me asking if we might add this conversion as well.

[DominiqueMakowski]

Maybe qnorm(0.95)?

[bwiernik]

Let me look into it—it's not obvious to me what the theory is behind that value (and the meta-analysis literature is rife with junk conversions, so I start off skeptical)

[mattansb]

Closing this as there seems to be no need (and also we now have an exact transformation when supplying p0).