Differences in Beta coefficients for interaction terms.

[Karen Wood]

Hi
I
To obtain significance levels for B and beta for females as well as males I re-coded males and females. However, the betas obtained for the interaction terms were different. Why is this and what does it mean?

Karen

[Swank, Paul R]

I assume you are using a regression model and are coding the categorical variables yourself. Consider:

 

Y = b0 + b1X + b2S + b3SX

 

Where S = 1 for male and 0 for female.

 

Then for females, the model is : Y = b0 + b1X

For males:                                        Y = (b0 + b2) + (b1+b3)X

 

So that b3 is the difference in slopes between males and females.

 

Suppose you recode S to be 5 for females and 2 for males;

 

Then for females : Y = b0 + 5 + (b1 + 5b3)X

And for males:        Y = b0 + 2 + (b1 + 2b3)X

 

Now 5b3 - 2b3 represents the difference in slopes or 3b3. Thus, the parameter changes but so does the standard error so that the t test remains the same.

 

Dr. Paul R. Swank,

Professor and Director of Research

Children's Learning Institute

University of Texas Health Science Center-Houston

 

From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Karen Wood
Sent: Tuesday, May 12, 2009 9:05 PM
To: [hidden email]
Subject: Differences in Beta coefficients for interaction terms.

 

Hi
I
To obtain significance levels for B and beta for females as well as males I re-coded males and females. However, the betas obtained for the interaction terms were different. Why is this and what does it mean?

Karen