# [R] Confidence interval for coefficient of variation

From: Kevin Wright <kw.statr_at_gmail.com>
Date: Thu, 14 Jun 2007 08:41:45 -0500

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)
}

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu 14 Jun 2007 - 13:56:29 GMT

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