Posted by
Maguin, Eugene on
Jul 18, 2012; 6:26pm
URL: http://spssx-discussion.165.s1.nabble.com/odds-ratio-to-chi-square-conversion-tp5713894p5714294.html
I wanted to thank all that have replied and especially Ryan, via Bruce, for responding with the Chinn article. In the process i found out something that I didn't know because I ran a simulation yesterday. Chinn said that the normal equivalent deviate, the 'NED', which I think is the same as the d statistic [(m1-m1)/sd], given that sd=1.0, is proportional to the logit, [Ln(odds)], in the range -2 = NED = 2. The proportionality constant being pi/sqrt(3), i.e., NED = logit/(pi/sqrt(3)) or NED = logit/1.8138. I am interested in the situation with a continuous predictor, 'x'. My little simulation showed that d = sd(x)*Ln(odds) to within a few tenths of a percent. So, different from Chinn.
Gene Maguin
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of Bruce Weaver
Sent: Monday, July 16, 2012 3:19 PM
To:
[hidden email]
Subject: Re: odds ratio to chi square conversion
Ryan is correct. From the article
(
http://www.aliquote.org/pub/odds_meta.pdf):"The standard logistic distribution [7] has variance pi^ 2/3, so a difference in ln(odds) can be converted to an approximate difference in NED [i.e., Normal equivalent deviate] by dividing by pi / SQRT(3), which is
1.81 to 2 decimal places."
I /suspect/ that the R function I mentioned in the other thread uses this method.
R B wrote
>
> *Correction:
>
> sd = pi / sqrt(3) ~ 1.81
>
> Ryan
>
> On Jun 30, 2012, at 4:38 PM, R B <ryan.andrew.black@> wrote:
>
>> Rich,
>>
>> I haven't read the article, but my guess is that they suggested
>> dividing by 1.81 since that value approximates the standard deviation
>> of the standard logistic distribution, which is pi/3.
>>
>> Ryan
>>
>> On Sat, Jun 30, 2012 at 3:46 PM, Rich Ulrich <rich-ulrich@> wrote:
>>
>> That's an interesting note. I'm not sure why it makes good sense, to
>> divide the ln(OR) by 1.81. But the writer does make good sense in
>> suggesting that a good measure of effect size is log(OR), and what
>> you need for further information is not the N, but the standard
>> error. (I think he is suggesting that.)
>>
>> The original question was about converting an OR to a chi-squared
>> test, in the context of meta-analysis.
>> I doubt why anyone should want to do that, except as an intermediate
>> step to finding the error term -- the chi-squared statistic itself is
>> a *test* statistic, and is poorly suited for "effect size". Where it
>> is appropriate, the OR is a fine measure of effect, and log(OR) is
>> the version that serves as an interval-scaled measure.
>>
>> --
>> Rich Ulrich
>>
>>
>> Date: Sat, 30 Jun 2012 07:44:43 -0700
>> From: srmillis@
>> Subject: Re: odds ratio to chi square conversion
>> To: SPSSX-L@.UGA
>>
>> FYI:
>>
>>
http://www.ncbi.nlm.nih.gov/pubmed/11113947>>
>> ~~~~~~~~~~~
>> Scott R Millis, PhD, ABPP, CStat, PStat® ...
>>
>
-----
--
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