### Background

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, as I can work out from R documentation and any wider reading I have done, the best performing methods for the CIs.

### Menu

- confidence interval of a proportion: requires the numerator and denominator counts.
- confidence interval of a difference between two (independent) proportions: requires the four numbers.
- confidence interval of a mean from mean, s.d. (or s.e.) and dataset size (
*n*). - confidence interval around an observed SD or variance: requires the observed value and
*n*. - 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 correlation coefficient. Requires observed value and
*n*. - Program to compute the confidence interval around an observed Spearman correlation coefficient. Requires observed value and
*n*. (I used to think the Pearson formula was good enough but there is a better equation used here.) - confidence interval around quantiles of a distribution given the data and quantiles you want. Plots the ECDF (Empirical Cumulative Distribution Function) showing the quantiles and their CIs.

###### Historical note 24.viii.20

Most of these calculators depended on an R package, CGIwithR, which was retired back around 2020. I’m keeping this note here because it did fantastic service for people for I I suspect two decades and for me for nearly that long 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 (https://shiny.rstudio.com/) 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.

#### About this page

Page built from things in the old psyctc.org site 4.i.19, updated 3.iv.24. All content is made available under the Creative Commons, CC BY-SA licence. Please feel free to reuse anything here but respect the licence, i.e. give attribution back to here.