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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


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