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# RE: st: Testing the extent of difference between two coefficients in the same model

 From Erik Aadland To Subject RE: st: Testing the extent of difference between two coefficients in the same model Date Mon, 30 Jan 2012 13:13:20 +0000

```Thanks again, Maarten and David.

I infer from your answer, Maarten, that I cannot test coeff1 > coeff2.
The "new" and "old" covariates measure the extent of a new context characteristic and an old context characteristic. In my post-estimation the p-value is .998

I also tried David's suggestion and changed the model. When adding the "new MINUS old" covariate and the "old" covariate in the same model, I get a positive significant coefficient for the "new MINUS old" covariate. However, in this model the "old" coefficient also turns positive and significant. David says that my covariate of interest is the "new MINUS old". This covariate operates as expected (postive and significant). But what to make of the "old" coefficient that is now significant? How to interpret this when "old" has also been subtracted from my main covariate of interest?

Regards,

Erik.

> Date: Mon, 30 Jan 2012 13:38:28 +0100
> Subject: Re: st: Testing the extent of difference between two coefficients in the same model
> From: maartenlbuis@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> On Mon, Jan 30, 2012 at 1:16 PM, Erik Aadland wrote:
> > 1. The example at the bottom of the FAQ tests for H0: coeff1 >= coeff2. Is it possible to test for H0: coeff1 > coeff2? If so, how?
>
> No, a null hypothesis must always contain an equal sign.
>
> > 2. Following the suggested example in the FAQ, I first run:
> >
> > test new-old = 0
> >
> > To calculate the appropriate p-value after having performed the Wald-test, I then run:
> >
> > local sign_new = sign(_b[new]- _b[old])
> > display "H0: new coeff >= old coeff. p-value = " normal(`sign_new'*sqrt(r(chi2)))
> >
> > If the resulting p-value is larger than .05 (e.g if it is .233), I interpret this such that I cannot reject the H0. In other words, I conclude that coeff_new is >= than coeff_old.
> >
> > The second question is: Is this the correct interpretation of the test?
>
> Almost. The interpretation is correct until the statement " I conclude
> that coeff_new is >= than coeff_old". You can only say that there is
> insufficient evidence to reject it. Remember that absence of evidence
> is not evidence of absence. It could just mean, and in all likelihood
> that is exactly the case, that your sample is just too small to detect
> that effect.
>
> Also consider David's comment
> <http://www.stata.com/statalist/archive/2012-01/msg01134.html> that
> these parameters are effects after adjusting for the other variables.
> If both old and new are just different ways of measuring the same
> concept than that would be a big problem: What does it mean when you
> say "a unit change in a measurement of variable x leads to b units
> change in y while keeping another measure of the same variable x
> constant"?
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
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