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emreliability (version 1.0.0)

spearman_brown: Spearman–Brown Prophecy Formula

Description

Compute the predicted test reliability after changing test length, or compute the required test-length ratio to achieve a desired reliability, using the Spearman–Brown prophecy formula.

Usage

spearman_brown(rxx, input, type = c("r", "l"))

Value

A named list depending on type:

reliability

Predicted reliability of the new test (if type = "r").

ratio

Required ratio of new test length to original test length (if type = "l").

Arguments

rxx

A numeric value indicating the original reliability (must be between 0 and 1, exclusive).

input

A numeric value indicating either:

  • the ratio of new test length to original test length (if type = "r"), or

  • the desired reliability of the new test (if type = "l").

type

Character string specifying the calculation type:

"r"

Compute new reliability given the length ratio.

"l"

Compute the length ratio required to achieve a desired reliability.

Details

The Spearman–Brown prophecy formula is: $$r_{yy} = \frac{k r_{xx}}{1 + (k - 1) r_{xx}},$$ where \(r_{xx}\) is the original reliability and \(k\) is the ratio of the new test length to the original test length.

Solving for \(k\) gives: $$k = \frac{r_{yy}(1 - r_{xx})}{r_{xx}(1 - r_{yy})}.$$

Examples

Run this code
spearman_brown(0.7, 3.86, "r")
spearman_brown(0.7, 0.90, "l")

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