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

 From "Lachenbruch, Peter" To "statalist@hsphsun2.harvard.edu" Subject RE: st: Testing the extent of difference between two coefficients in the same model Date Mon, 30 Jan 2012 08:02:51 -0800

```Not quite.  This would imply a one-sided alternative leading (still) to aa test of equality but with the alternative in the favored direction.  Maybe a simpler way would be to compute a confidence interval (one-sided).

________________________________________
From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis [maartenlbuis@gmail.com]
Sent: Monday, January 30, 2012 4:38 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Testing the extent of difference between two coefficients in the same model

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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