# Roger Palay copyright 2016-02-20
# Saline, MI 48176
#
ci_2popvar <- function (
             n_top, s_top, n_bot, s_bot,
             cl=0.95)
{ # generate a confidence interval for the  ratio
  # of the top variance to the bottom variance from
  # a sample of the top population with size n_top 
  # and standard deviation s_top and a sample of the
  # bottom population with size n_bot and standard 
  # deviation s_bot.  cl gives the confidence level.

alpha <- 1-cl
alphadiv2 <- alpha/2
v_top <- s_top^2
v_bot <- s_bot^2
quotient <- v_top / v_bot
xlow <-  qf( alphadiv2, n_top-1,n_bot-1)
xhigh <- qf( alphadiv2, n_top-1,n_bot-1,
            lower.tail=FALSE)
c_low <- quotient/xhigh
c_high <- quotient/xlow

result <- c( c_low, c_high, quotient,
             xlow, xhigh, v_top,
             s_top, n_top, v_bot, s_bot,
             n_bot, cl, alphadiv2)
names(result) <-
          c( "CI Low", "CI_HIGH", "Quotient",
             "F Low",  "F High",  "Top Var.",
             "Top sd", "Top size", "Bot Var.",
             "Bot sd", "Bot size", "C level",
             "Alpha/2")
return( result)
}