Computation background

This uses the function getRCIfromSDandAlpha() in my CECPfuns R package but the maths is trivial and straight out of the original work on the RCI.

Maths of the RCI

Ignore this next bit if you don't like equations!

The full equation is:

The equation is:

SD * sqrt(2) * sqrt(1 - rel) * qnorm(1 - (1 - ci) / 2)

The MathJax typesetting of the equation is a bit ugly:

$$SD*\sqrt{2}*\sqrt{1-rel}*qnorm(1 - \frac{(1 - ci)}{2})$$

where 'SD' is the SD you input, 'rel' the reliability you input and 'ci' the inclusion interval you wanted, usually .95, i.e. 95% and 'qnorm' is the quantile of the standard Gaussian/Normal distribution for that ci.

So if you asked for the usual 95% interval that simplifies to this:


because 1.96 is the value of the standard Gaussian that maps to 95% inclusion


If you have the raw item data and n > 20 I recommend you compute the Cronbach alpha internal reliability for your own data. I will put up an app to compute that for raw item data when I can.

Next please ...

Unless you are very familiar with it, please now go to the 'Background' tab and read the information there.


App created by Chris Evans licenced under a Creative Commons, Attribution Licence-ShareAlike Please respect that and put an acknowledgement and link back to here if re-using anything from here.

Citing and referencing

I really am not keen on the obsessionalities of style guides but I do think referencing well is important so here is my understanding of the correct citing and referencing of the app.


I think the correct citation in APA 7 format is just (Evans, 2023) and the reference format is:

Evans, C. (2023, September 17). Compute RCI from SD and reliability. Retrieved April 17, 2024, from

Where the name of the app, i.e. 'Compute RCI from SD and reliability' should be in italics. (Hard to force that here in HTML!)


I am sure the correct citation in BPS format is again just (Evans, 2023) and I think the BPS reference format is:

Evans, C. (2023). Compute RCI from SD and reliability. Retrieved April 17, 2024, from

Where the name of the app is not in italics.

But, as I say, I am no expert on these style guide obsessionalities: as with everything in, use at your own risk and do sensible checking.

Background and related resources

This shiny app is one of a growing number in, my shiny server
They complement:

There is a form if you want to contact me: so do please use that if you think there is anything wrong here or anything that could be improved.

There is also now an Email announcement list, never updating more than monthly, where I will put up developments of new apps here, a summary of updates to the glossary and new posts in the Rblog. You can sign up for that here.