Testing for the Independence of Continuous Variables

[Ethan Gunn]

Hi all,

I am wondering if there is a way in STATA to test for/prove that two continuous variables are independent of each other. I am new to statistics so any help would be appreciated.

The one thing I can think of is using the corr command to produce a value of Pearson's correlation coefficient, like so:

. corr inf sasy
(obs=128)

inf sasy

inf 1.0000
sasy -0.4855 1.0000


This displays a negative correlation, but is there some sort of threshold, or burden of proof, with the Pearson coefficient that would sufficiently show that the two variables are independent? Is this just p=0?

Thanks,
Ethan

[Rich Goldstein]

first, unless you orthogonalized the data, the likelihood of getting a correction of 0 is just about 0; second, statistics deals with a stochastic world so that you don't "prove" anything about the real world with statistics; third, and most important, I think you are not asking your real question and you need to do so to get a helpful answer; in particular, I don't understand why anyone needs to "test/prove that two continuous variables are independent" - why would you care? why do you want to test this?

[Ethan Gunn]

Thanks Rich. You are right. The real issue I am having is in testing for cointegration. I am told that when testing for cointegration between the dependent and a single independent variable in a multi variate time-series regression, the relationships between each of the independent variables must be independent for the Engle-Granger tests to have salience. Is this correct? I am not so sure. In any case, my ultimate goal was to find a way to justify using non-stationary variables in time series, and so I looked to find evidence of cointegration.

Thanks

[Rich Goldstein]

sorry, but I know next-to-nothing about cointegration; maybe someone else can help