# This R code computes sample sizes needed 
# to obtain specified power for a test of 
# the null hypothesis that two proportions
# are equal.  It also computes sample sizes
# needed to obtain confidence intervals with 
# specified margin of error. This code is 
# posted as   power2p.R

# Specify the probability of success 
# for the first population        
  p1 <- .58 

# Specify the probability of success 
# for the second population         
  p2 <- .50

# Enter power values    
  power <- c(.8, .9, .95, .99) 

# Ener the type I error level
  alpha <- .05         

  za <- qnorm(1-alpha/2)
  za1 <- qnorm(1-alpha)
  nb <- length(power)
   p <- (p1+p2)/2
  va <- p1*(1-p1)+p2*(1-p2)
  rp <- sqrt(2*p*(1-p)/va)
 
 
# Obtain a sample size for each of
# the requested power values

     zb <- qnorm(power)
     size <- ((za*rp+zb)^2)*va/((p1-p2)^2)
     size1 <- ((za1*rp+zb)^2)*va/((p1-p2)^2)

# Increase sample size to next largest integer
# and print results

  sizer <- ceiling(size)
  size1r <- ceiling(size1)

   cat("\n \n Sample sizes for testing equality of two proportions",
       "\n \n \n p1=",p1,"p2=", p2, "alpha=",
       alpha,"power=", power,
    "\n \n        Sample sizes (2-sided test): " , sizer,
    "\n \n \n \n p1=",p1,"p2=", p2, "alpha=",
       alpha,"power=", power,
  "\n \n       Sample sizes (1-sided test): " , size1r, "\n") 

# Compute sample size needed to obtain a
# confidence interval for the difference
# between the two proportions with a 
# specified margin of error   

# Enter the confidence level
  level <- c(0.95)     

# Enter desired margin of error 
  me <- c(0.04, .02, .01)

# Compute needed sample sizes

  alpha2  <- (1.0-level)/2
  np <- length(me)
  one <- rep(1,np)  

  n <-((qnorm(one-alpha2)/me)^2)*va
  n <- ceiling(n)

  percent <- level*100;

  cat("\n \n \n Sample sizes for ", percent,
  " percent confidence intervals: \n",
  "\n \n margin of error: ", me, 
  " \n \n sample size:     ", n, "\n")