# Significant interaction in linear model with Pearson r as possible explanation

I have tested gender difference on the relationship between Variable A and B using linear model (GLM command in SPSS).

I have found that the interaction of A (covariate/independent variable) with gender (factor) on B (dependent variable) is statistically significant. This means that the relationship between A and B differ based on whether one is a male or a female.

I am not familiar with GLM procedure, so I am wondering what is the next step.

Question 1: Is there a way to find out whether the difference in the relationship between A and B is greater for males over females or vice versa. (i.e. how do I interpret the difference?)

My preference is to just stop at this stage and look at the correlation coefficients between A and B for males and females separately and based on the GLM result, discuss the two coefficients. e.g. if r for males is 0.64 and r for females is 0.72, then I just conclude, based on the GLM, that the correlation is stronger for females over males.

Question 2: Is it possible to combine GLM and correlation (Pearson) in the above manner?

Your thoughts will help me better explain the findings to my target audience!

• How is your outcome variable distributed? Try graphing outcome vs. predictor. Compare the slope of the predictor for males and females. – Michael Bishop Nov 16 '11 at 15:00
• Yes, perhaps a graphic illustration will be better. Can I do this in SPSS ver 17 – Adhesh Josh Nov 17 '11 at 22:21

Let Y be your DV, X be your independent continuous variable (covariate), G be grouping factor (gender, 1=male, 2=female). You want to know how males differ from females in dependency of Y on X.

GLM Y BY G WITH X /DESIGN= X G X*G /PRINT= PARAM.


Look in Parameter estimates table.

• Intercept = intercept in regression of Y on X for females.
• Coefficient for G=males = intercept in regression of Y on X for males minus intercept in regression of Y on X for females.
• Coefficient for X = regression coefficient of Y on X for females.
• Coefficient for interaction G=males * X = regression coefficient of Y on X for males minus regression coefficient of Y on X for females. Thus, if this value is positive then b for males is higher than b for females; and its significance is the significance of this difference in b.
• Thanks Does Pearson r have any merit in this approach. (I think the answer is no, based on your response!) – Adhesh Josh Nov 15 '11 at 20:13
• In your simple situation (one X) consulting with r is justified. In general situation (several Xs) the answer is no. – ttnphns Nov 16 '11 at 6:05