Partial Correlation

[kim.barchard]

Hi everyone,

I have a question about partial correlation.  My hand calculations don't
agree with SPSS.

I am calculating the partial correlation between y and b, when a has been
partialled out.  All cases have complete data on these three variables.

r-squared for predicting y based on a = r2y.a = .1232.
r-squared for predicting y based on a and b = r2y.ab = .1634.

Howell (2007) states that the squared partial correlation (r-squared for
predicting y based on b, when a has been partialled out of both y and b) =
r2yb.a = (r2y.ab - r2y.a) / ( 1- r2y.a)
This is (.1634 - .1232) / (1 - .1232) = .0458
To calculate the partial correlation, I took the square root of this, and I
got .2141.

In SPSS, I used
PARTIAL CORR   /SIGNIFICANCE=TWOTAIL   /MISSING=LISTWISE   /VARIABLES= y b
BY a.
and I got .3335
I can also calculate the squar of this to get the squared partial
correlation, and I get .3335^2 = .1112.

Is my hand calculation wrong?  Is SPSS wrong?

Thank you for your help,

Kim

[Dominic Lusinchi]

Your formulas are incorrect, as far as I can tell. The partial correlation
between y and x1 controlling for x2 is

ryx1|x2 = [ryx1 - (ryx2*rx1x2)] / [SQRT(1-{rx1x2}^2)*SQRT(1-{ryx2}^2)]

in which ryx1 = correlation of y with x1; ryx2 = correlation of y with x2;
rx1x2 = the correlation of x1 and x2; and "8" the multiplication symbol and
"^" the exponentiation symbol.

Dominic Lusinchi
Statistician
Far West Research
Statistical Consulting
San Francisco, California
415-664-3032
www.farwestresearch.com


-----Original Message-----
From: [hidden email] [mailto:[hidden email]]
Sent: Friday, January 12, 2007 10:54 AM
Subject: Partial Correlation

Hi everyone,

I have a question about partial correlation.  My hand calculations don't
agree with SPSS.

I am calculating the partial correlation between y and b, when a has been
partialled out.  All cases have complete data on these three variables.

r-squared for predicting y based on a = r2y.a = .1232.
r-squared for predicting y based on a and b = r2y.ab = .1634.

Howell (2007) states that the squared partial correlation (r-squared for
predicting y based on b, when a has been partialled out of both y and b) =
r2yb.a = (r2y.ab - r2y.a) / ( 1- r2y.a)
This is (.1634 - .1232) / (1 - .1232) = .0458
To calculate the partial correlation, I took the square root of this, and I
got .2141.

In SPSS, I used
PARTIAL CORR   /SIGNIFICANCE=TWOTAIL   /MISSING=LISTWISE   /VARIABLES= y b
BY a.
and I got .3335
I can also calculate the squar of this to get the squared partial
correlation, and I get .3335^2 = .1112.

Is my hand calculation wrong?  Is SPSS wrong?

Thank you for your help,

Kim

[kim.barchard]

Dear Dominic,

I checked a few other sources, and I found them relatively evenly divided
in terms of which formula they give.  Hays (1994) gives both formulas.  I
re-did my calculations, and they now agree.  I think I put different
variables for b when I did the two calculations.

Thanks for the help,

Kim



Dominic Lusinchi <[hidden email]> writes:

Your formulas are incorrect, as far as I can tell. The partial correlation
between y and x1 controlling for x2 is

ryx1|x2 = [ryx1 - (ryx2*rx1x2)] / [SQRT(1-{rx1x2}^2)*SQRT(1-{ryx2}^2)]

in which ryx1 = correlation of y with x1; ryx2 = correlation of y with x2;
rx1x2 = the correlation of x1 and x2; and "8" the multiplication symbol and
"^" the exponentiation symbol.

Dominic Lusinchi
Statistician
Far West Research
Statistical Consulting
San Francisco, California
415-664-3032
www.farwestresearch.com


-----Original Message-----
From: [hidden email] [mailto:[hidden email]]
Sent: Friday, January 12, 2007 10:54 AM
Subject: Partial Correlation

Hi everyone,

I have a question about partial correlation.  My hand calculations don't
agree with SPSS.

I am calculating the partial correlation between y and b, when a has been
partialled out.  All cases have complete data on these three variables.

r-squared for predicting y based on a = r2y.a = .1232.
r-squared for predicting y based on a and b = r2y.ab = .1634.

Howell (2007) states that the squared partial correlation (r-squared for
predicting y based on b, when a has been partialled out of both y and b) =
r2yb.a = (r2y.ab - r2y.a) / ( 1- r2y.a)
This is (.1634 - .1232) / (1 - .1232) = .0458
To calculate the partial correlation, I took the square root of this, and I
got .2141.

In SPSS, I used
PARTIAL CORR   /SIGNIFICANCE=TWOTAIL   /MISSING=LISTWISE   /VARIABLES= y b
BY a.
and I got .3335
I can also calculate the squar of this to get the squared partial
correlation, and I get .3335^2 = .1112.

Is my hand calculation wrong?  Is SPSS wrong?

Thank you for your help,

Kim