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.