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# Re: st: question about the interaction term

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: question about the interaction term Date Thu, 25 Apr 2013 11:08:21 +0200

```On Thu, Apr 25, 2013 at 10:33 AM, ZHVictor <victerzj2@hotmail.com> wrote:
> OK, I am thinking the basic idea of the paper is even the small and insignificant change can lead to a large change in significance level
Applying it to my example, it means even the interaction term is
insignificant, the coefficient of A may be insignificant in B=1 case
even thought it is significant in B=0 case. Thus, if I only look at
the insignificant interaction term, I may conclude that the
coefficient of A is still significant in B=1 case as in B=0 case.  So
it means even though the interaction term is insignificant, it may
still be able to change the significance level of A.

The authors start from another position: they see a common mistake of
the form "effect of variable A is significant in group B=1 and
insignificant in group B=0 and _therefore_ the effect of A is
different between groups B=1 and B=0". In order to determine whether
the effects are different one needs to look at the significance of the
interaction term.

> For my case, I need to know two things. First, whether the coefficient of A is significant in B=0 case. Second, whether the coefficient of A is significant in B=1 case. Thus, for the B=0 case, it is easy to see the significance of A in the regression. However, for B=1 case, the coefficient of A becomes the coefficient of A+the coefficient of A*B. Therefore, I should test A+A*B=0. Right?

Correct, but make sure that noone interprets the result that one
effect is significant and the other is insifinicant as "the effect of
A in group B=1 is different from the effect of A in group B=0".

You may also be interested in: M.L. Buis (2012) "Stata tip 106: With
or without reference", The Stata Journal, 12(1), pp. 162-164. This
discusses how you can obtain the results you want directly.

>> > One more question is if the coefficient of A is -0.4 and the coefficient for the interaction is 0.2, so the coefficient of A in B=1 case should be -0.4+0.2=-0.2 but not -0.4+0=-0.4. Is that correct?
>>
>> I don't understand that question, where did the 0 come from?
>
> Since the interaction term is insignificant， I can treat it as 0. That is where the 0 comes from.

Insignificant just means that you cannot reject the hypothesis that
the coefficient is 0. In statistical testing "not rejecting" is not
the same as "accepting". In fact, we can never accept an hypothesis.
So the statement that insignificant means you can treat a coeficient
as 0 is false.

-- Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
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