[R] Effect size, interactions, and main effects (Stats Question) [ffmanova]

Robert A LaBudde ral at lcfltd.com
Sat Jul 21 16:00:23 CEST 2007

Statistical significance is "detectability", and depends upon the 
size of the  sample as well as the effect. A large enough experiment 
will result in statistical detectability of almost every interaction 
action term allowed.

This is why estimation, not testing, has become the consensus 
recommendation in statistics.

As a practical matter, evaluate the combined effect of your model 
terms with and without the interaction term(s) you are worried about. 
Is the reduction in accuracy of physical importance? If so, the 
interaction terms are required for scientific reasons. If not, 
present both results and indicate the acceptability (for 
interpolation) of the simpler model.

You should also make it your first priority to hypothecate why the 
interaction terms are meaningful and expected. If a cause can be 
found, it may suggest an alternate model that will eliminate 
interactions, or satisfy your anxiety. If not, it may support your 
argument to simplify.

At 08:58 AM 7/21/2007, Mark wrote:

>Dear List Members,
>I would very much appreciate any pointers you could give me on the following
>Main Question:
>To what extent does the "rule" that it is unreasonable to talk about main
>effects if there are significant interactions in a model depend upon effect
>size [of the significant interaction terms]?  Or is this not an issue?
>More practically:  Suppose I were to carry out a so-called Type-II MANOVA
>(using ffmanova) and were to find that the interaction term in a 2-way
>analysis has borderline significance (say p = 0.045) and a small effect
>size, whereas one of the main effects is highly signficant (say p = 6.8e-10)
>and has a large effect size.
>Would it in this case be reasonable for me to ignore the interaction term,
>and talk only about main effects?  And, presuming the main question is fair,
>are there general guidlines concerning the relationship between level of
>significance and effect size for interaction terms.
>Thank you in advance for your help,

Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
Least Cost Formulations, Ltd.            URL: http://lcfltd.com/
824 Timberlake Drive                     Tel: 757-467-0954
Virginia Beach, VA 23464-3239            Fax: 757-467-2947

"Vere scire est per causas scire"

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