[R] power.anova.test for interaction effects

[Andrew Kniss]

It's a rather complex model.  A 37*4 factorial (37 cultivars[var]; 4
herbicide treatments[trt]) with three replications[rep] was carried out at
two locations[loc], with  different randomizations within each rep at each
location.

Source           DF   Error Term      MS
Loc               1   Trt*rep(loc)    12314
Rep(loc)          4   Trt*rep(loc)    1230.5
Trt               3   Trt*rep(loc)    64.72
Trt*loc           3   Trt*rep(loc)    33.42
Trt*rep(loc)     12   Residual        76.78
Var              36   Var*trt*loc     93.91
Var*trt         108   Var*trt*loc     12.06
Var*trt*loc     144   Residual        43.09
Residual        575   NA              21.23
  

-----Original Message-----
From: Bob Wheeler [mailto:bwheeler at echip.com] 
Sent: Monday, February 21, 2005 4:33 PM
To: akniss at uwyo.edu
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] power.anova.test for interaction effects

Your F value is so low as to make me suspect your model. Where did the 
144 denominator degrees of freedom come from?

Andrew Kniss wrote:

> 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
> 
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-- 
Bob Wheeler --- http://www.bobwheeler.com/
         ECHIP, Inc. ---
Randomness comes in bunches.