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

[BERNARD L COHEN <blc+@PITT.EDU>]

On Mon, 3 Jun 2002, Kai Kaletsch wrote:



> 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.



	--My computer code couldn't handle the above, so I ran:

	100 smokers   100 lung cancers

	 99 	      101

	101 	      102



The result was R-squared = 25%, which is not bad (coeff of correlation =

0.5), about the same as for regression of lung cancer on smoking. But the

slope of the regression has a standard deviation of 170% of the slope,

which means that the relation is meaningless. It is this percentage Std

Dev of the slope that is important. It is quite small for lung cancer vs

smoking, contrary to claims to the contrary. See my paper in Statistics in

Medicine 14:327-328;1995

	These matters are discussed at some length in my paper in Health

Physics 72:489-490;1997.



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