Stat 141  Single classification Analysis of Variance: power and sample size, 

Power calculations via power.anova.test (see web page references)

Review: use power.anova.test for 2 group case of one-way anova  (repeat 10/31 exs)          
> power.anova.test(groups =2, power = .8, between.var = .08, sig.level = .05, 
     within.var = 1) #efsize=.4      
Balanced one-way analysis of variance power calculation 
         groups = 2                                     
              n = 99.08033                              
    between.var = 0.08                                  
     within.var = 1                                     
      sig.level = 0.05                                  
          power = 0.8                                   
 NOTE: n is number in each group                        
> power.anova.test(groups =2, power = .8, between.var = .125, sig.level = .05, 
      within.var = 1) ##efsize = .5              
  Balanced one-way analysis of variance power calculation        
         groups = 2                                              
              n = 63.76561                                       
    between.var = 0.125                                          
     within.var = 1                                              
      sig.level = 0.05                                           
          power = 0.8                                            
 NOTE: n is number in each group 



k = 1:6                                 
> power.anova.test(groups =4, n=5*k, between.var = 1, sig.level = .05, within.var=3) 
     Balanced one-way analysis of variance power calculation 
         groups = 4
              n =  5, 10, 15, 20, 25, 30
    between.var = 1
     within.var = 3
      sig.level = 0.05
          power = 0.3535594, 0.7096896, 0.8957212, 0.9679022, 0.9911867, 0.9977856
 NOTE: n is number in each group 

> var(c(1.5,1.8,3.2,3.5)) #4 means             > var(c(1.38,2,3,3.62)) #4 means  
[1] 0.9933333                                  [1] 1.002933                     

> power.anova.test(groups =4, n=5*k, between.var = 1, sig.level = .01, within.var = 3) 
     Balanced one-way analysis of variance power calculation 
         groups = 4
              n =  5, 10, 15, 20, 25, 30
    between.var = 1
     within.var = 3
      sig.level = 0.01
          power = 0.1392961, 0.4516311, 0.7258003, 0.8856526, 0.9584920, 0.9864935
 NOTE: n is number in each group