# getRelBySpearmanBrown: Function using the Spearman-Brown formula to predict... In cpsyctc/CECPfuns: Package of Utility Functions for Psychological Therapies, Mental Health and Well-being Work (Created by Chris Evans and Clara Paz)

## Description

Function using the Spearman-Brown formula to predict reliability for new length or get length for desired reliability

## Usage

 1 2 3 4 5 6 getRelBySpearmanBrown( oldRel, lengthRatio = NULL, newRel = NULL, verbose = TRUE ) 

## Arguments

 oldRel numeric: the reliability you have lengthRatio numeric: the ratio of the new length to the old length newRel numeric: the desired reliability verbose logical: whether to give messages explaining the function

## Value

numeric: either predicted reliability or desired length ratio (whichever was input as NULL)

## background

This is ancient psychometrics but still of some use. It has been checked against two functions in the psychometric package with gratitude. For more information, see:

The formula is simple:

^*=\fracn\rho1 + (n-1)\rho

The short summary is that any multi-item measure will have overall internal reliability/consistency that is a function of the mean inter-item correlations and the number of items and, for any mean inter-item correlation, a longer measure will have a higher reliability. The formula for the relationship was published separately by both Spearman in 1910 and in the same year by Brown, who was working for Karl Pearson, who had a running feud with Spearman. See:

That also gives some arguments that the formula should really be termed the Brown-Spearman formula but I am bowing to historical precedent here.

## History/development log

Started before 5.iv.21, updated help page 10.iv.21.

Chris Evans

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ## Not run: ### if you had a reliability of .8 from a measure of, say 10, items, ### what reliability might you expect from one of 34 items? getRelBySpearmanBrown(.8, 3.4) ### if you had a reliability of .7 from 10 items how much lower ### would you expect the reliability to be from a measure of only 5 items? ### from examples for psychometric::SBrel() with respect and gratitude! getRelBySpearmanBrown(.7, .5, verbose = FALSE) ### if you have a reliability of .7, how much longer a measure do you expect ### to need for a reliability of .9? ### again with acknowledgement to psychometric::SBlength() with respect and gratitude! getRelBySpearmanBrown(.7, lengthRatio = NULL, .9) ## End(Not run) 

cpsyctc/CECPfuns documentation built on April 15, 2021, 3:26 a.m.