Power and Sample Size for one-way ANOVA

### Power and Sample Size for one-way ANOVA

# Alternative Situation:
among 4 means, 2 are the same
the smallest is delta/2 smaller
the largest is delta/2 bigger

# Sample Size

sample_size <- function(n, beta){
  K<-4
  delta<-20
  sigma<-60
  alpha<-0.05

  # critical value
  f <- qf(0.95,K-1,n*(K-1)) 

  # noncentrality parameter
  ncp <- n*delta^2/(2*K*sigma^2) 

  # Pr{ F(ncp) < f } - beta 
  pf(f,K-1,n*(K-1),ncp) - beta 
} 

# sample size satisfying power = 1-beta
uniroot(sample_size, c(10,10000), beta=0.2)$root