[R] Confidence interval for coefficient of variation

[Kevin Wright]

This is a function I coded a few years ago to calculate a confidence
interval for a coefficient of variation.  The code is based on a paper
by Mark Vangel in The American Statistician.  I have not used the
function much, but it could be useful for comparing cv's from
different groups.

Kevin Wright


confint.cv <- function(x,alpha=.05, method="modmckay"){
  # Calculate the confidence interval of the cv of the vector x
  # Author: Kevin Wright
  # See: Vangel, Mark.  Confidence Intervals for a Normal Coefficient
  # of Variation. American Statistician, Vol 15, No1, p. 21--26.
  # x <- c(326,302,307,299,329)
  # confint.cv(x,.05,"modmckay")

  x <- na.omit(x)
  v <- length(x)-1
  mu <- mean(x)
  sigma <- sqrt(var(x))
  k <- sigma/mu
  # CV > .33 may give poor results, so warn the user
  if(k>.33) warning("Confidence interval may be very approximate.")

  method <- casefold(method) # In case we see "McKay"

  if(method=="mckay"){
    # McKay method.  See equation 15.
    t1 <- qchisq(1-alpha/2,v)/v
    t2 <- qchisq(alpha/2,v)/v
    u1 <- v*t1
    u2 <- v*t2
    lower <- k/sqrt(( u1/(v+1) -1)*k*k + u1/v)
    upper <- k/sqrt(( u2/(v+1) -1)*k*k + u2/v)
  } else if (method=="naive"){
    # Naive method.  See equation 17.
    t1 <- qchisq(1-alpha/2,v)/v
    t2 <- qchisq(alpha/2,v)/v
    lower <- k/sqrt(t1)
    upper <- k/sqrt(t2)
  } else {
    # Modified McKay method. See equation 16.
    u1 <- qchisq(1-alpha/2,v)
    u2 <- qchisq(alpha/2,v)
    lower <- k/sqrt(( (u1+2)/(v+1) -1)*k*k + u1/v)
    upper <- k/sqrt(( (u2+2)/(v+1) -1)*k*k + u2/v)
  }
  ci <- c(lower,upper)
  attr(ci,"CV") <- k
  attr(ci,"alpha") <- alpha
  return(ci)
}