Confidence interval calculators

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Update note 24.viii.20

Most of these calculators depended on an R package, CGIwithR, which as far as I can see has been retired. It did fantastic service for I suspect two decades so I’m incredibly grateful to David Firth for his work on it. The best way forward for online interactive R apps is now the shiny system ( which is brilliant but, for me at least, comes with a stiff learning curve and I really need to install it on my own server to be able to do all I want to with it, including replacing my old apps. This is all work in progress but other things keep having higher priority so I’m not sure when this will get moving well again. Sadly, this means that only the Cronbach alpha app is working as of now.


I’m not sure when I first started mounting these calculators, certainly by 2003. These compute the confidence interval (CI) for observed sample statistics using the sample statistics and the sample size. The default CI is 95% but you can set other spreads if you want them. For continuous value statistics these are parametric model CIs based on Gaussian distributions, for rates these are the best performing methods for the CIs as far as I can work out from R documentation and my reading).

  • confidence interval of a proportion Mounted 12.viii.03.
  • confidence interval of a difference between two (independent) proportions Mounted 14.viii.03.
  • confidence interval of a mean from mean, s.d. (or s.e.) and sample size (n). Mounted 16.viii.03, last updated 22.xii.03.
  • confidence interval for Cronbach’s alpha from the observed value, n and the number of items (k).  
  • Program to compute the confidence interval around an observed (Pearson or Spearman) correlation coefficient. Requires observed value and n.