Re: st: Statistical Significance of the difference between two estimates from two separate regressions

[David Hoaglin <dchoaglin@gmail.com>]

Hi, Andri.

I agree with the suggestion of using a single regression.  In many
situations, using a pooled estimate of the residual variance will give
you greater power in testing whether the return to schooling differs
between males and females.  And, as Billy Buchanan pointed out, that
approach will allow you to do more.

Doing the first test that John Antonakis suggested does not depend on
whether the education variable is continuous.

Since the education variable is continuous (not the usual choice, I
think), you should investigate whether the effect of education is
linear.  It may not be.  If education is measured in years, you can
examine its effect by converting the "continuous" variable into a set
of categories, perhaps as detailed as single years if you have a large
enough sample size, and then plot the coefficients for those
categories against the corresponding number of years (or the midpoint
of the category, if you use multi-year categories).  If the pattern in
that plot is not linear, it may suggest a suitable functional form,
such as a linear spline.

David Hoaglin

On Fri, Mar 14, 2014 at 8:16 AM, Kyrizi, Andri <ak196@leicester.ac.uk> wrote:
> Dear Mr Hoaglin,
>
> Thank you for your helpful comments.
> Yes the two regressions have exactly the same sets of predictors and my education variable is continuous.
>
> So your suggestion would be to use a single regression? Or since my education variable is continuous I can do the first test that Professor Antonakis suggested?
> (my main 'concern' is to test whether the return to schooling for males is statistically different to that of females)
>
> All the best,
> Andri
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