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

getRelBySpearmanBrown(
oldRel,
lengthRatio = NULL,
newRel = NULL,
verbose = TRUE
)

## Arguments

oldRel numeric: the reliability you have numeric: the ratio of the new length to the old length numeric: the desired reliability 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:

${\rho^{*}}=\frac{n\rho}{1 + (n-1)\rho}$

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

if (FALSE) {
### 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)
}