Re: odds ratio to chi square conversion

[Maguin, Eugene]

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

 

[Kornbrot, Diana]

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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[Rich Ulrich]

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

 

[Maguin, Eugene]

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

 

[Bruce Weaver]

Gene, apparently someone has written an R function for going in the opposite direction -- from ln(OR) to Cohen's d.  

  http://rgm2.lab.nig.ac.jp/RGM2/func.php?rd_id=compute.es:lor_to_es

Perhaps you can find something by digging around on that site (or contacting the maintainer).

HTH.

Maguin, Eugene wrote

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]<mailto:[hidden email]>
Subject: Re: odds ratio to chi square conversion
To: [hidden email]<mailto:[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

[Rich Ulrich]

Two samples separated by 0.5 SD will have their
overlap of histograms at z +/-  0.25.

My convenient normal table tells me that a z-score
of 0.25 (half of 0.5) contains about 10% of the area.

So the implied sample separation is 60/40 vs. 40/60 --
  OR = 3600/1600 = 9/4 = 2.25.
 
If you don't have the formulas handy to manipulate
(or maybe, even if you do), the easy way to find
what the equation would be is to dummy up some
100 lines of data to be approximately Normal(0, 1);
adjust to mean=0 exactly; multiply by 10 to create
variance= 100; then add 45 to half, 50 to the other
half, for Group 1 and 2.  Then run logistic on it.

--
Rich Ulrich

---

Date: Mon, 16 Jul 2012 14:18:14 -0400
From: [hidden email]
Subject: Re: odds ratio to chi square conversion
To: [hidden email]

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.

[Maguin, Eugene]

It’s always good to simulate data as a check and I did that.

This is the means by group.

Report
Y
X	N	Mean	Std. Deviation
0	500	47.49995676	10.000003703
1	500	52.49998532	10.000006021
Total	1000	49.99997104	10.303219145

 

Correlations
		Y
X	Pearson Correlation	.243
	Sig. (2-tailed)	.000
	N	1000

 

Now the logistic regression

Variables in the Equation
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	.000	.063	.000	1	1.000	1.000

 

Variables in the Equation
		B	S.E.	Wald	df	Sig.	Exp(B)
Step 1a	Y	.050	.007	55.668	1	.000	1.051
	Constant	-2.503	.342	53.666	1	.000	.082

 

 

 

 

 

 

 

From: Rich Ulrich [mailto:[hidden email]]
Sent: Monday, July 16, 2012 3:28 PM
To: Maguin, Eugene; SPSS list
Subject: RE: odds ratio to chi square conversion

 

Two samples separated by 0.5 SD will have their
overlap of histograms at z +/-  0.25.

My convenient normal table tells me that a z-score
of 0.25 (half of 0.5) contains about 10% of the area.

So the implied sample separation is 60/40 vs. 40/60 --
  OR = 3600/1600 = 9/4 = 2.25.
 
If you don't have the formulas handy to manipulate
(or maybe, even if you do), the easy way to find
what the equation would be is to dummy up some
100 lines of data to be approximately Normal(0, 1);
adjust to mean=0 exactly; multiply by 10 to create
variance= 100; then add 45 to half, 50 to the other
half, for Group 1 and 2.  Then run logistic on it.

--
Rich Ulrich

---

Date: Mon, 16 Jul 2012 14:18:14 -0400
From: [hidden email]
Subject: Re: odds ratio to chi square conversion
To: [hidden email]

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 [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.