Re: st: test of significant between coefficients

[Nick Cox <njcoxstata@gmail.com>]

Richard's answer overlaps with mine, which is fine.

I want to underline the idea that often coefficients should be thought
as being bundled together. For example, if a cosine term is included
in a model a sine term should be too. Leaving out one or the other can
omit some useful information about phase even if one coefficient is
not significant. A more widely familiar example is a set of
indicators. Degrading them so that all are significant just coarsens a
model.

Come to think of it, we've have had this discussion before. Just
search for "Richard Williams" in the Statalist archives.

Nick

On Tue, Sep 27, 2011 at 3:48 PM, Richard Williams
<richardwilliams.ndu@gmail.com> wrote:
> At 10:35 AM 9/27/2011, Andrea Rispoli wrote:
>>
>> Dear Statalisters,
>> I am running a test of significance between two coefficients of the
>> same OLS regression.
>> My question is : if the two coefficients are not significant, does it
>> still make sense to conduct the test? I am asking because sometimes
>> while the individual coefficients are not significant the difference
>> between them is significant, so I was trying to understand the meaning
>> of this result.
>> Thank you!
>> AR
>
> It can happen. The individual tests are testing whether the coefficients
> equal zero. The equality test might be testing whether, say, -.5
> significantly differs from .5. In any event, there is nothing that says all
> your tests have to be logically consistent with each other. The overall F or
> chi-square statistic might be significant for a model, while none of the
> individual coefficients are.
>
> A more common situation might be where a coefficient is significant in one
> group but not in another. I always warn my students to be careful about
> saying X is important for one group but not the other. If, say, you are
> comparing whites and black, your white sample size might be much larger,
> which can help the effect to achieve significance for whites but not blacks.
> The actual estimated coefficients, however, may be quite similar.
>
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