Comparison of beta coefficients within the same group

I have a question, to which I have found some answers from different sources, but never really applicable to my problem.

So, I have measured how Var1 predicts Var2 (beta = .14)
Then, I have measured how Var1 predicts Var2 while controlling for Var3 (beta = .12).

How can I measure if the beta coefficients (.14 and .12) are statistically different from each other? This is within the same group.

Can I use the graphcial way (Cumming, 2009), where you inspect how much the CI's overlap....? Or is there an easier way?

Thank you in advance!


Not a robit
Well I am sure there is an easy way/test, but this is not my expertise area. You could potentially looked at the partial R^2 values with confidence intervals on them. I know there are eta and omega squared values for these estimates and not sure if one does a better job of adjusting for changes in R^2 solely related to the number of terms in the model.

In the field of epidemiology, they typically look for a 10% change in estimates as a sign of confounding. Also, I wonder if you could just create 10,000 bootstrap samples and run the models on each sample and calculate all of the differences, than plot them and find the 95% percentile confidence intervals for differences.


Not a robit
A slight point of clarification, sobel examines mediated effects, i was referencing confounding, and you also have backdoor paths from controlling for common effects and interaction issues. It is best to try and draw out the proposed relationships.