[R] power.anova.test for interaction effects

[Andrew Kniss]

Using the data set posted at 
http://uwstudentweb.uwyo.edu/A/AKNISS/sbxherb.txt
I obtained this output from R:

> data(sbxherb)
> attach(sbxherb)
> sbxherb$rep<-factor(c("I","II","III"))
> sbxherb$var<-factor(sbxherb$var)
> sbxherb$trt<-factor(sbxherb$trt, labels=c("Check","Early","Late","Micro"))
> detach(sbxherb)
> attach(sbxherb)
> aov.sbx<-aov(yield~rep + trt * var + Error(rep/(trt+var)))
> summary(aov.sbx)

Error: rep
    Df  Sum Sq Mean Sq
rep  2 122.158  61.079

Error: rep:trt
          Df  Sum Sq Mean Sq F value Pr(>F)
trt        3 201.131  67.044  1.3096  0.355
Residuals  6 307.160  51.193               

Error: rep:var
          Df Sum Sq Mean Sq F value    Pr(>F)    
var       36 4613.9   128.2  8.4392 1.425e-14 ***
Residuals 72 1093.5    15.2                      
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

Error: Within
           Df  Sum Sq Mean Sq F value Pr(>F)
trt:var   108  956.62    8.86  0.9731 0.5574
Residuals 216 1966.04    9.10


I would like to use this output to help design next years study, which will
be carried out with the same design.  However, I would like to know what the
sample size should be in order to have an 80% chance of finding a 10%
difference in the interaction term trt:var at alpha=0.05.  Is there a way to
coerce power.anova.test() to make this calculation for me?  I have tried
using this function to give me the sample size needed to find differences
given the within and between groups variance from the previous study, but
with no success.  If I have it calculate the power from this data set, it
tells me I have a power of 1, which I doubt is true given the high p-value
and wide confidence intervals around the estimates.

> power.anova.test(groups=148,
+                  sig.level=0.05,
+                  power=0.8,
+                  within.var=9.10,
+                  between.var=8.86)
Error in uniroot(function(n) eval(p.body) - power, c(2, 1e+05)) : 
        f() values at end points not of opposite sign
> power.anova.test(groups=148,
+                  sig.level=0.05,
+                  n=3,
+                  within.var=9.10,
+                  between.var=8.86)

     Balanced one-way analysis of variance power calculation 

         groups = 148
              n = 3
    between.var = 8.86
     within.var = 9.1
      sig.level = 0.05
          power = 1

 NOTE: n is number in each group


Any help is greatly appreciated.  I apologize if I seem to be nagging on
this issue, but I thought this post was much better at describing what I am
after.  Thanks in advance.

Andrew Kniss
University of Wyoming
akniss at uwyo.edu




-----Original Message-----
From: Andrew Criswell [mailto:andrew at arcriswell.com] 
Sent: Tuesday, February 22, 2005 9:30 PM
To: akniss at uwyo.edu
Subject: Re: [R] power.anova.test for interaction effects

Dear Andrew,

If you could supply us with your data, more help would possibly be 
forthcoming.

Best wishes,
Andrew

Andrew Criswell, PhD
Graduate School, Bangkok University