# 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