Re: odds ratio to chi square conversion

Posted by Kornbrot, Diana on Jul 16, 2012; 9:54am
URL: http://spssx-discussion.165.s1.nabble.com/Re-odds-ratio-to-chi-square-conversion-tp5714198p5714242.html

Suspect the answer in general is NO
This is because logit is based on proportions which are only determined by mean & sd if populationdistribution type is known
A classic problem is decrease in a continuous property like cognitive ability with age [cross-sectional]
If the older group has lower mean is this because all people have declining ability with age? Or because the older group has a higher proportion of people with ability lowering disease?

Obviously, the diligent researcher should have checked for normality, but the reader usually  has no way of checking. If, and only if, both groups have normal distribution then proprotions are predictable from mean & sd and hence logit regression parameters are calculable. Standard t/F tests only tell you that investigators ASSUMED normality, not hether it acutally happened

Back to calculate N for sem. In my view these are very much estimates and one is only as good as one’s weakest  link. So it is N for the least powerful effect that matters. The sem input correlation matrix, in my view, should have all correlations of the same type. We had some trouble when some correlations were Pearson’s r and some polychoric, as the polychoric’s tend to be lower.  Others will be wiser on estimating N for sem than I am & I would dearly love some good references

Best

Diana


On 13/07/2012 15:17, "Maguin, Eugene" <emaguin@...> wrote:

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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