estimate_length_sb {psychmeta}

Inverse Spearman-Brown formula to estimate the amount by which a measure would have to be lengthened or shorted to achieve a desired level of reliability

Description

This function implements the inverse of the Spearman-Brown prophecy formula and answers the question: "How much would I have to increase (do decrease) the length of this measure to obtain a desired reliability level given the current reliability of the measure?" The result of the function is the multiplier by which the length of the original measure should be adjusted. 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_length_sb(rel_initial, rel_desired)

Arguments

rel_initial

Initial reliability of a measure.

rel_desired

Desired reliability of a lengthened or shortened measure.

Details

This is computed as:

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

where \rho_{XX} is the inital reliability, \rho_{XX}^{*} is the predicted reliability of a measure with a different length, and k^{*} is the number of times the measure would have to be lengthened to obtain a reliability equal to \rho_{XX}^{*}.

Value

The estimated number of times by which the number of items in the initial measure would have to be multiplied to achieve the desired reliability.

References

Ghiselli, E. E., Campbell, J. P., & Zedeck, S. (1981). Measurement theory for the behavioral sciences. San Francisco, CA: Freeman. p. 236.

Examples

## Estimated k to achieve a reliability of .8 from a measure with an initial reliability of .7
estimate_length_sb(rel_initial = .7, rel_desired = .8)

## Estimated k to achieve a reliability of .8 from a measure with an initial reliability of .9
estimate_length_sb(rel_initial = .9, rel_desired = .8)