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

[Maarten buis <maartenbuis@yahoo.co.uk>]

--- 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:

If you want to know the mean then you would need at least one 
observation.

If you want to know an effect, then you need at least two 
observation: one from group 1, one from group 2, and the 
difference (or ratio) of the means in each groups is the 
effect.

If you want to know an interaction effect, then you need 
at least four observation: two in group A and two in group B,
and with each group one for group 1 and one for group 2. 
Within each A and B group you estimate the difference between 
groups 1 and 2, and than you look at whether this effect in
Group A is different from this effect in Group B.

So the information on interaction effect that is present in
the data is much more indirect than the information on effect,
which in turn is more indirect than the information on central 
tendency. The consequence of that is that you need more data
to get a reliable estimate of an interaction effect then you 
need to get a regular effect, and that comes back in the 
standard errors. 

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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