Test on correlation?

1. May 26, 2010

zli034

Say I have 2 separate predictor variables x and y.

And the response variable is z. The correlation between x and z is a; the correlation between y and z is b.

How to get the p-value for a = b? By using SAS or SPSS.

I believe we should use t-test. Because the correlation analysis for only 1 correlation is significant or not is compared to 0 by t-test.

I kind have some ideas to work this out on paper, but it is complicated to perform and consider normality, variances, and degree of freedom. I'm looking for a software package to do this simply.

2. May 27, 2010

EnumaElish

You should be able to "trick" the software, by running the regression

Z = b0 + b1 D + b2 W + b3 X + u

where
Z = [z z]'
D = [0 1]'
W = [y x]'
X = [0 x]'
0 is the zero vector
1 is a vector of 1's (sometimes called a summation vector)
u is the random error.

The t statistic of b3 is a test of whether the regression coefficient on y is different from that on x. However, a regression coefficient is not the same as a correlation coefficient, although they are very similar; and you'll need to scale your data (with the appropriate standard deviation ratio) to manipulate the software to produce a correlation coefficient "under the guise" of a regression coefficient.

Last edited: May 28, 2010
3. May 27, 2010

zli034

What is the theory behind this?

4. May 28, 2010

EnumaElish

To be general about it, the "theory" is the linear regression model, or even more generally, linear optimization. However, I suspect you are asking a more specific question. The model I've suggested is a shortcut for performing the Chow test for pooling of two datasets.

Last edited: May 28, 2010
5. May 28, 2010

zli034

Cool. I'll beware of this Chow test