---
title: "Spearman-Brown formula"
description: "Also known as the Spearman-Brown \"prediction\" or even \"correction\" formula and apparently there's an argument that it should be Brown-Spearman, but I've never seen it that way round. #### Details The formula tells you that, if you have the internal…"
url: "https://www.psyctc.org/psyctc/glossary2/spearman-brown-formula/"
updated: "2024-05-03"
category: All OM book glossary entries
---

# Spearman-Brown formula

Also known as the Spearman-Brown "prediction" or even "correction" formula and apparently there's an argument that it should be Brown-Spearman, but I've never seen it that way round.

#### Details

The formula tells you that, if you have the internal reliability of a multi-item measure, what internal reliability, all things being equal, the measure would have had it more or fewer items. Like this:

![](https://www.psyctc.org/psyctc/wp-content/uploads/2024/05/graphic1-1-1024x630.png)

The formula does make the assumption that the different length instrument would behave the same way which is almost certainly not the case, however, the predictions are probably a sensible guide and the best we can have in the absence of actual empirical data for the other lengths. See my Rblog for a bit more information and shiny app if you want to play with the predictions the formula makes.

#### Try also

Cronbach's coefficient alpha
Internal reliability
Reliability

#### Chapters

The issue of lengths of measures is touched on in Chapter 4 but the formula is not discussed: too geeky!

#### Online resources

More detail in my [Rblog](https://www.psyctc.org/Rblog/index.html): entry [here](https://www.psyctc.org/Rblog/posts/2021-04-09-spearman-brown-formula/).
App in [my shiny apps](https://shiny.psyctc.org/) which computes the predictions for you [here](https://shiny.psyctc.org/apps/Spearman-Brown/).

#### Dates

First created 3.v.24.