Re: Cohen's Ecologic Studies (R-squared)

[Kai Kaletsch <info@eic.nu>]

Bill,



I agree that in a study of anything vs. lc it is a good idea to "account"

for smoking. What I don't understand is how a low R-squared value has

anything to do with being able to "account" or not account for smoking. I

was hoping you could explain it on my specific example.



In the example, the R-squared will be fairly low for any smoking-lc relation

that you want to propose. That doesn't mean your smoking-lc relation is

wrong or that it can't "account" for lc.



Kai



----- Original Message -----

From: <epirad@mchsi.com>

To: "Kai Kaletsch" <info@eic.nu>

Cc: <radsafe@list.vanderbilt.edu>

Sent: Monday, June 03, 2002 10:31 AM

Subject: Re: Cohen's Ecologic Studies (R-squared)





> Kai,

>

> If you hope to determine if the relationship is linear

> or not between radon exposure and lung cancer, you need

> to be able to account for smoking.  I would have more

> confidence that he could account for smoking if he was

> able to show that his surrogate measures for county

> averaged smoking rates could at least help to predict

> the lung cancers within the county.  The low r-squared

> value indicates to me that he is not able to adequately

> account for smoking.

>

> Bill Field

> > OK - we might not be able to agree on everything, but we should be able

to

> > agree on the meaning of a simple statistical indicator, such as the

> > R-squared value. Please consider the following:

> >

> > 3 counties, each with 3 million people. The number of smokers and lc

deaths

> > per unit time (what ever that is) is as follows:

> >

> > County 1 has 1 000 000 smokers and 10000 lc deaths.

> > County 2 has 1 000 001 smokers and 9900 lc deaths.

> > County 3 has 1 000 002 smokers has 10120 lc deaths.

> >

> > Perhaps Drs. Cohen and Field could both calculate the R-squared value (I

> > think its pretty small) and explain how this value is related to the

ability

> > to "account" for lc due to smoking.

> >

> > (To me, this data doesn't show anything about a smoking-lc relationship,

but

> > it doesn't disprove it either. The fact that R-squared is small gives no

> > clue about the correctness or incorrectness of anything. It just says

that

> > it is a poor data set to use if you want to draw a conclusion about a

> > smoking-lc relationship. It might be a good dataset, if you are looking

at

> > an "anything else-lc" relation.)

> >

> > Thank You,

> > Kai, the poor miner trying to understand this stuff

> >

> > ----- Original Message -----

> > From: "BERNARD L COHEN" <blc+@PITT.EDU>

> > To: <EPIRAD@mchsi.com>

> > ....

> > >>  As for Dr. Cohen's

> > > > ecologic analyses, he can account for only about 30% of

> > > > the lung cancer mortality with his smoking data.

> > >

> > > --Wrong, wrong, wrong. The fact that R-squared is only 30% derives

> > > from the small up and down statistical variations. The true indication

of

> > > predictability is the standard deviation of the slope of the

regression of

> > > lung cancer on smoking prevalence which is very small percentage-wise

> > ....

> >



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