psychmeta (version 2.7.0)

estimate_rel_sb: Spearman-Brown prophecy formula to estimate the reliability of a lengthened measure

Description

This function implements the Spearman-Brown prophecy formula for estimating the reliability of a lengthened (or shortened) measure. The formula implemented here assumes that all items added to (or subtracted from) the measure will be parallel forms of the original items.

Usage

estimate_rel_sb(rel_initial, k)

Value

The estimated reliability of the lengthened (or shortened) measure.

Arguments

rel_initial

Initial reliability of a measure.

k

The number of times by which the measure should be lengthened (if k > 1) or shortened (if k < 1), assuming that all new items are parallel forms of initial items.

Details

This is computed as:

$$\rho_{XX}^{*}=\frac{k\rho_{XX}}{1+(k-1)\rho_{XX}}$$

where \(\rho_{XX}\) is the initial reliability, k is the multiplier by which the measure is to be lengthened (or shortened), and \(\rho_{XX}^{*}\) is the predicted reliability of a measure with a different length.

References

Ghiselli, E. E., Campbell, J. P., & Zedeck, S. (1981). Measurement theory for the behavioral sciences. San Francisco, CA: Freeman. p. 232.

Examples

## Double the length of a measure with an initial reliability of .7
estimate_rel_sb(rel_initial = .7, k = 2)

## Halve the length of a measure with an initial reliability of .9
estimate_rel_sb(rel_initial = .9, k = .5)