# Roger Palay copyright 2016-01-31
# Saline, MI 48176
#
hypoth_2test_prop <- function(
       x_one, n_one, x_two, n_two,
       H1_type, sig_level=0.05)
{ # perform a hypothsis test for the difference of
  # two proportions based on two samples.
  # H0 is that the proportions are equal, i.e.,
  # their difference is 0
  # The alternative hypothesis  is
  #      !=  if H1_type =0
  #      <   if H1_type < 0
  #      >   if H1_type > 0
  # Do the test at sig_level significance.
  phat_one <- x_one / n_one
  phat_two <- x_two / n_two
  phat <- (x_one+x_two) / (n_one+n_two)
  std_err <- sqrt( phat*(1-phat)*(1/n_one +1/n_two) )
  diff <- phat_one - phat_two
  if( H1_type==0)
     { z <- abs( qnorm(sig_level/2))}
  else
     { z <- abs( qnorm(sig_level))}
  to_be_extreme <- z*std_err
  decision <- "Reject"

  if( H1_type < 0 )
     { crit_low <-   - to_be_extreme
       crit_high = "n.a."
       if( diff > crit_low)
         { decision <- "do not reject"}
       attained <- pnorm( diff, mean=0, sd=std_err)
       alt <- "p_1 < p_2"
     }
  else if ( H1_type == 0)
     { crit_low <-  - to_be_extreme
       crit_high <-   to_be_extreme
       if( (crit_low < diff) & (diff < crit_high) )
          { decision <- "do not reject"}

       if( diff < 0 )
         { attained <- 2*pnorm(diff, mean=0, sd=std_err)}
       else
         { attained <- 2*pnorm(diff, mean=0, sd=std_err,
                             lower.tail=FALSE)
         }
       alt <- "p_1 != p_2"
     }
  else
     { crit_low <- "n.a."
       crit_high <-  to_be_extreme
       if( diff < crit_high)
         { decision <- "do not reject"}
       attained <- pnorm(diff, mean=0, sd=std_err,
                         lower.tail=FALSE)
       alt <- "p_1 > p_2"
     }

 result <- c( alt,  n_one, x_one, phat_one,
                    n_two, x_two, phat_two,
                    phat, std_err, z,
                    crit_low, crit_high, diff,
                    attained, decision)
 names(result) <- c("H1:",
                    "n_one","x_one", "phat_one",
                    "n_two","x_two", "phat_two",
                    "pooled", "Std Err", "z extreme",
                    "critical low", "critical high",
                    "difference",
                    "attained", "decision")
 return( result )
}