Thanks, Rich. My question is how. For instance, suppose x is a true-enough dichotomy and y is a continuous variable.
Let
n(1) = 50; mean(1) = 45; SD(1) = 10
n(2) = 50; mean(2) = 50; SD(2) = 10
Analyzed as a t-test, the standard ‘d’ effect size is 0.5.
But, what would the computation to get, most importantly, the corresponding OR and, secondarily, the intercept?
Thanks, Gene
From: Rich Ulrich [mailto:[hidden email]]
Sent: Monday, July 16, 2012 2:01 PM
To: Maguin, Eugene; SPSS list
Subject: RE: odds ratio to chi square conversion
Diana K. emphasized the problem of assumptions.
But, to turn assertion around the other way -- If you make
assumptions about normality, you surely can get estimates
of the coefficients of the simple logistic regression.
And I say "about normality" because assuming that they
are "normal" is not the only choice. You could assume
some degree of skewness (say), and use Monte Carlo
randomizations to estimate what the LR results would be
under various assumptions.
However, it does seem to me that the "effect sizes" in
terms of mean differences, etc., is what you will need
for any power analysis, rather than the LR results.
--
Rich Ulrich
Date: Fri, 13 Jul 2012 10:17:43 -0400
From: [hidden email]
Subject: Re: odds ratio to chi square conversion
To: [hidden email]
Thanks to all that responded. I understand the problem that Diana pointed out, that there is not a one-to-one correspondence between OR and chi-square. I didn’t know that before.
What I’d like to ask about now is this specific situation: the association between a dichotomous variable and a continuous variable. The association could be expressed as a t/F value or (point biserial) correlation or as an odds ratio (OR). The choice depends on which variable is thought of as the dependent. Given sufficient summary information (e.g., Ns, means, SDs by group) can a t/F/r analysis be manipulated to extract the B0 and B1 (intercept and slope) coefficients in a logistic regression (or probit regression)? (To better focus responses, I understand that there is not a one-to-one correspondence between either OR or ln(OR) and phi. I did a little simulation to check.)
For what it’s worth, the context for all this is not a meta-analysis per se but a summary of relationships between pairs of variables that will feed into a power analysis for an SEM model that includes both dichotomous and continuous variables.
Gene Maguin
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