# OLS: checking the whether the difference between two variables is significant

• Jul 27th 2013, 06:59 AM
Elena1990
OLS: checking the whether the difference between two variables is significant
Hi everybody!

I have a question about hypothesis testing in ordinary least squares regressions. I have 4 OLS regression coefficients and I know each of their standard errors. They are b1, b2, b3, and b4.

What I am trying to figure out is if (b1-b2) - (b3-b4) is statistically significant from zero. Does that make sense? I have been able to find sources saying how to test whether the difference between to coefficients is significant, but I am trying to test whether the difference between the difference in 4 coefficients is significant. Let me know if I need to explain this better! I really appreciate the help,

Elena
• Jul 27th 2013, 05:18 PM
chiro
Re: OLS: checking the whether the difference between two variables is significant
Hey Elena1990.

There are a few ways to do this. One way is through contrasts and the other way is through a variety of results relating to specific statistics (like 2-sample t-tests and their extension) along with asymptotic and approximate statistics.

If you are using something like SAS, you can specify a contrast that will test your hypothesis and give you a p-value (and a test statistic). The statement you use is the contrast statement.

Are you using a computer package?
• Jul 27th 2013, 05:44 PM
Elena1990
Re: OLS: checking the whether the difference between two variables is significant