I could easily see a reason to test for interactive effects even when main
effects are not significant.
Take for example motor insurance and a model that tries to predict who will
have an accident.
Consider and extreme example to make a point.
factor 1: two groups of cars one with the break pedal at a normal
distance from the driving seat and another car designed for people with
long legs.
factor 2: height - small and tall - splitting the population 50%/50%
If we further assume that cars are dished out randomly between tall and
small people, then of course there will be lots of accidents, however you
will spot nothing when just looking at the main factors. For example half
the small people crash due to being in tall peoples cars and vice versa.
Likewise half of each lot of cars crash due to being driven by people with
the wrong length legs!
However the interactive effect will ofcourse tell everything!
Slightly exaggerated but I could imagine this in real life too.
I'd be interested to hear what field you are using these models in.
THIS E-MAIL ORIGINATED FROM THE INTERNET - Please read the detailed
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Dear Statisticians
When building a multivariate model to test for associations between an
outcome variable and multiple factors, I tend to avoid testing for a
significant interactive effect between two factors if I have already found
that the main effects for the corresponding factors are not statistically
significant.
Nevertheless, I am conscious that there is some lack of consensus amongst
statisticians as to whether this is an appropriate approach to take. I
would be interested therefore to receive individual views (together with
explanations) as to whether or not the above approach is justifiable.
The above issue is strongly related to the question of what to conclude if
an interactive effect proves to be significant in a multivariate analysis
when neither of the main effects were significant. I would therefore very
much welcome some suggestions here too!
Many thanks
Best wishes
Margaret
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