[R] power.anova.test for interaction effects

[Andrew Kniss]

This question will probably get me in trouble on theoretical grounds, but I
will pose it anyway.

The situation:
I recently ran a field study looking for differences in sugarbeet cultivar
tolerance to a specific herbicide.  The study was set up so that 37
cultivars were treated with 4 different applications of the herbicide (37*4
factorial).  In doing so, we found that the interaction effect was highly
insignificant (ndf=108, ddf=144, F=0.28, p=1.0000).  Now my problem is
this... the study takes up an enormous amount of time, energy, and money (as
you could guess with 37 cultivars in a field study).  We need to determine
weather it is worth the effort to repeat the study this summer (practically,
it is not, but our funding source would like a more concrete demonstration).

I decided to try using power.anova.test just as a starting point to see what
our power was.  My question is: is this valid to do on an interaction term?
If I use power.anova.test with on the interaction term, this is what I get:

~>  power.anova.test(groups=(37*4), n=3, between.var=12.06,
~+                  within.var=21.23, sig.level=0.05)
~
~     Balanced one-way analysis of variance power calculation 
~
~         groups = 148
~              n = 3
~    between.var = 12.06
~     within.var = 21.23
~      sig.level = 0.05
~          power = 1
~
~ NOTE: n is number in each group 


This would imply that given the variability we observed with 3 replications,
we almost certainly would have found differences if they existed.  But given
what I have read on power analysis, a high p-value and wide confidence
intervals nearly always suggest inadequate sample size. (Our 90% confidence
intervals differed from the estimates by as much as 28%, when a 10%
difference would be significant from a practical perspective.) 

So is this a valid approach? Or does the power.anova.test fall apart if
using an interaction effect? 

Thank you in advance for any help or references you are willing to point me
to.
Best regards,
Andrew Kniss
Assistant Research Scientist
University of Wyoming
Department of Plant Sciences
1000 E. University Ave.
Laramie, WY  82071  USA

akniss at uwyo.edu