Re: st: Re: Why main effects are significant but interction term is not signficant

[Richard Williams <richardwilliams.ndu@gmail.com>]

At 07:49 AM 3/8/2011, Maarten buis wrote:
> --- On Tue, 8/3/11, Mike wrote:
> >  y= beta+beta1*x1+beta2*x2+beta3*x1*x2+epsilon
> >
> > You can think of y as income, x1 is gender (1 for male) and
> > x2 is the educational level.
> >
> >  The OLS gives a significant results for beta1 and beta2
> > but not beta3. In the context of the example, male and higher
> > education help having higher income. But the interaction of
> > male and higher education doesn't have any significant effect
> > on income.
>
> That is possible, and in smaller to medium size studies even
> likely. Interaction effects typically require very large
> datasets before they become significant. You can see that by
> looking at the absolute minimum number of observations
> necessary to get an estimate:

Also, my suspicion (possibly wrong) is that interaction effects will 
tend to be smaller than main effects and hence harder to detect in a 
sample. For example, I can envision a world in which the effect of X 
on Y is 5 for men and 6 for women. In a reasonably large sample, it 
won't be too hard to detect that, for both groups, the effect of X 
differs quite a bit from zero. But, it will be much more difficult to 
determine that there is a significant difference between the effects 
in the 2 populations. Put another way, it takes a larger N to detect 
small effects than it does to detect large effects.


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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