# Roger Palay copyright 2016-03-04
# Saline, MI 48176
#
hypoth_2test_var <- function(
       n_top, s_top, n_bot, s_bot,
       H1_type, sig_level=0.05)
{ # perform a hypothsis test for equality of
  # the variances of two populations
  # based on two samples of n_top and n_not
  # items yielding sample
  # standard deviations s_top and s_bot
  #  where the alternative hypothesis  is
  #      !=  if H1_type==0
  #      <   if H1_type < 0
  #      >   if H1_type > 0
  # Do the test at sig_level significance,
  #
  # It is important that the population is a normal
  # distribution.

  decision <- "do not reject"
  v_top = s_top^2
  v_bot = s_bot^2
  quotient <- v_top / v_bot
  alpha <- sig_level
  if ( H1_type == 0 )
     { alpha <- alpha/2 }
  #find the critical value(s)
  xlow <- qf(alpha,n_top-1,n_bot-1)
  xhigh <- qf( alpha, n_top-1, n_bot-1,
               lower.tail=FALSE)
  if( H1_type == 0 )
    {  if( (quotient < xlow) | (quotient>xhigh) )
         { decision <- "Reject" }
       if (quotient < 1 )
         { attained = 2*pf(quotient,n_top-1,n_bot-1)}
         else
         { attained = 2*pf(quotient, n_top-1,
                          n_bot-1, lower.tail=FALSE) }
       H1 <- "v_1 != v_2"
    }
    else if( H1_type < 0 )
    {  if( quotient < xlow )
         { decision <- "Reject" }
       attained = pf( quotient,n_top-1,n_bot-1)
       xhigh <- "n.a."
       H1 <- "v_1 < v_2"
    }
    else
    {  if( quotient > xhigh )
         { decision <- "Reject" }
       attained = pf( quotient,n_top-1,
                n_bot-1,lower.tail=FALSE)
       xlow <- "n.a."
       H1 <- "v_1 > v_2"
    }
   result <- c( H1, n_top, s_top, v_top,
             n_bot, s_bot, v_bot, quotient, xlow,
             xhigh, decision, attained )
   names(result) <- c( "H1","n top", "s top", "v top",
              "n bot", "s bot", "v bot",
              "quotient", "crit low", "crit high",
              "decision", "attained")
   return (result)
  }