**Date:** Tue, 13 Sep 2005 16:55:16 +0200
**Reply-To:** Marta García-Granero
<biostatistics@terra.es>
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
**From:** Marta García-Granero
<biostatistics@terra.es>
**Organization:** Asesoría Bioestadística
**Subject:** Re: Converting OR into Cohen's d statistic
**In-Reply-To:** <s32696de.075@GWMAIL01.LOYOLA.EDU>
**Content-Type:** text/plain; charset=ISO-8859-15
Hi Martin,

MS> A colleague approached me today and wanted to convert an
MS> Odds ratio into Cohen's d statistic. He indicated that he could do this
MS> by taking the log of the OR. Does anyone know if this is correct and if
MS> it is not is there a way of converting an OR into a d.

You can find the formula for logit d here:

http://www.apa.org/books/resources/kline/kline_over5.pdf

Basically:

logit(d)=log(OR)/1.8138

1.8138=pi/SQRT(3), to be more precise.

But...

MS> He is trying to do a meta analysis and wants to
MS> convert the report Odds Ratios into Cohen's d.

One criticism of meta-analysis is that it tries to mix apples with
oranges, with one lemon now and then. Although you can certainly put
Cohen's d-s and logit d-s (the measure you are looking for) in the same
bucket, shake it well and see what they turn into, I'd recommend your
colleague to keep them apart. One thing is comparing logit d values
with Cohen's d values (for different measures of the SAME 2 groups),
and other thing, quite different, is trying to combine them into a
chimerical overall measure, difficult to interpret in a practical way.

The correct way of meta-analysing several studies is trying to use a
common outcome measure (quantitative with quantitative, and
qualitative with qualitative). Don't mix apples with oranges, please.

If he only has OR to combine, then why doesn't he meta-analyse them
directly without turning them into logit d? The document I mentioned
above gives details about the advantages of using OR as an ES measure.

You can download a collection of meta-analytis syntax files I wrote at:

http://www.spsstools.net/Syntax/MetaAnalysis/META-SPSS.ZIP

Methods included are:

1. Meta-analysis of P values.

2. Meta-analysis of binary outcomes: RD, OR and RR, with both fixed & random
effects (DerSimonian-Laird) models. Raw data (counts) or summary data
(adjusted OR, RR or RD) can be used as input. Different fixed effects models:
inverse variance (Woolf method), Mantel-Haenszel and Peto (this last only
for OR) are available for raw data (counts); for summary data only the first.

3. Meta-analysis of continuous outcomes: unstandardised & standardised (Hedges,
Cohen & Glass) mean differences, with both fixed (inverse variance) & random
effects (DerSimonian-Laird) methods. Means, SD & N or Cohen's d can be used
for input (except for Glass method, which requires means, SD & N).
Orwin's Fail Safe N is computed for significant results.

4. Meta-analysis of correlation coefficients: Hedges-Olkin fixed & random
effects models (inverse variance & Dersimonian-Laird).
Orwin's Fail Safe N is computed for significant results.

5. Meta-analysis of correlation coefficients: Schmidt-Hunter method (simplified,
unreliability or range departure correction methods are not included).

More technical details can be found at:

http://www.spsstools.net/Syntax/MetaAnalysis/ReadMeFirst.txt

--
Regards,
Marta mailto:biostatistics@terra.es