Calculating confidence intervals for proportions

April 9, 2014

(This article was first published on Insights of a PhD student » R, and kindly contributed to R-bloggers)

Heres a couple of functions for calculating the confidence intervals for proportions.

Firstly I give you the Simple Asymtotic Method:

simpasym <- function(n, p, z=1.96, cc=TRUE){
  out <- list()
    out$lb <- p - z*sqrt((p*(1-p))/n) - 0.5/n
    out$ub <- p + z*sqrt((p*(1-p))/n) + 0.5/n
  } else {
    out$lb <- p - z*sqrt((p*(1-p))/n)
    out$ub <- p + z*sqrt((p*(1-p))/n)

which can be used thusly….

simpasym(n=30, p=0.3, z=1.96, cc=TRUE)
[1] 0.119348

[1] 0.480652


Where n is the sample size, p is the proportion, z is the z value for the % interval (i.e. 1.96 provides the 95% CI) and cc is whether a continuity correction should be applied. The returned results are the lower boundary ($lb) and the upper boundary ($ub).

The second method is the Score method and is define as follows:

scoreint <- function(n, p, z=1.96, cc=TRUE){
  out <- list()
  q <- 1-p
  zsq <- z^2
  denom <- (2*(n+zsq))
    numl <- (2*n*p)+zsq-1-(z*sqrt(zsq-2-(1/n)+4*p*((n*q)+1)))
    numu <- (2*n*p)+zsq+1+(z*sqrt(zsq+2-(1/n)+4*p*((n*q)-1)))
    out$lb <- numl/denom
    out$ub <- numu/denom
    if(p==1) out$ub <- 1
    if(p==0) out$lb <- 0
  } else {
    out$lb <- ((2*n*p)+zsq-(z*sqrt(zsq+(4*n*p*q))))/denom
    out$ub <- ((2*n*p)+zsq+(z*sqrt(zsq+(4*n*p*q))))/denom

and is used in the same manner as simpasym…

scoreint(n=30, p=0.3, z=1.96, cc=TRUE)
[1] 0.1541262

[1] 0.4955824

These formulae (and a couple of others) are discussed in Newcombe, R. G. (1998) who suggests that the score method should be more frequently available in statistical software packages.Hope that help someone!!!Reference:Newcombe, R. G. (1998) Two-sided confidence intervals for the single proportion: comparison of seven methods. Statist. Med., 17: 857-872. doi: 10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.C


To leave a comment for the author, please follow the link and comment on their blog: Insights of a PhD student » R. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)