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RE: st: RE: strange results with corr


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: strange results with corr
Date   Thu, 17 Feb 2005 16:32:01 -0000

It is simpler than you seem to fear. 
Think in terms of a scatter plot. With two dummy 
variables, the possible data points in 
general are the 4 corners of the unit
square. The correlation treating these
numerically will have modulus 1 if and 
only if the points populated in practice
are just the two opposite corners. 

That is, with 

	                 * 1,1 



	* 0,0 

the correlation would be 1, and with 

     * 0,1 





                       * 1, 0 

the correlation would be -1. In either 
case a straight line would be a perfect 
fit to the data, irrespective of how 
many data points fall on each corner, 
so long as some do. 

In practice, with your dataset data fall on 
3 out of 4 corners, and we can't say anything 
so simple: the result of the correlation 
will depend on the votes cast, as it were. 
With this election result 
 

    2458 


   11119    739 


the best-fit line would clearly tilt downwards, 
but fairly gently, so the correlation looks fine by me, 
qua correlation. 

Nick 
n.j.cox@durham.ac.uk 

Kenley Barrett
 
> I'm sorry, I should have included all possible counts. I have pasted
> them below. To be sure that I understand properly: this correlation
> coefficient is due the fact that although a value of 1 for wifelit
> guarantees a value of 0 for wifeprim, and a value of 1 for wifeprim
> guarantees a value of 0 for wifelit, a value of 0 for wifeprim does
> NOT guarantee a value of 1 for wifelit, and a value of 0 for wifelit
> does NOT guarantee a value of 1 for wifeprim. So the correlation
> coefficient should not be -1 (as I was thinking earlier). Could you
> please confirm for me that I'm understanding this right? I'm sorry to
> bother you again; I am new at this, as you can tell.
> 
> . count if wifelit == 1 & wifeprim == 1
>     0
> 
> . count if wifelit == 0 & wifeprim == 1
>  2458
> 
> . count if wifelit == 0 & wifeprim == 0
> 11119
> 
> . count if wifelit == 1
>   739
> 
> . count if wifeprim == 1
>  2458
> 
> 
> . count if wifelit == 1 & wifeprim == 0
>   739
> 
> . corr wifelit wifeprim
> (obs=14316)
> 
>              |  wifelit wifeprim
> -------------+------------------
>      wifelit |   1.0000
>     wifeprim |  -0.1062   1.0000
 
> On Thu, 17 Feb 2005 15:58:32 -0000, Nick Cox 
> <n.j.cox@durham.ac.uk> wrote:
> > You evidently have two dummies here, both 0 or 1.
> > 
> > You give two of the four possible
> > counts, from which we can infer that
> > in 14316 - 2458 cases the values are 1 0 or 0 0.
> > 
> > That seems entirely consistent with the correlation
> > you get. The entire 2 by 2 table from -tab wifeprim
> > wifelit- is the context for the correlation.
> > 
> > Nick
> > n.j.cox@durham.ac.uk
> > 
> > Kenley Barrett
> > 
> > > I am getting strange results when I run the "corr" command on my
> > > variables. From my understanding, "corr" gives the correlation
> > > coefficient, so if a value of 1 for Dummy Variable A guarantees a
> > > value of 0 for Dummy Variable B, then corr should give a 
> result of -1.
> > > But instead I am getting values between 0 and -1. A sample of two
> > > variables shown below:
> > >
> > > . count if wifelit == 1 & wifeprim == 1
> > >     0
> > >
> > > . count if wifelit == 0 & wifeprim == 1
> > >  2458
> > >
> > > . corr wifelit wifeprim
> > > (obs=14316)
> > >
> > >              |  wifelit wifeprim
> > > -------------+------------------
> > >      wifelit |   1.0000
> > >     wifeprim |  -0.1062   1.0000
> > >
> > > What could be the problem? Am I misunderstanding the corr command?

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