psychometric (version 2.4)

SpearmanBrown: Spearman-Brown Prophecy Formulae

Description

These two functions are various manipulations of the Spearman-Brown Prophecy Formula. They are useful in determining relibility if test length is changed or length of a new test if reliability were to change.

Usage

SBrel(Nlength, rxx)
SBlength(rxxp, rxx)

Value

rxxp

the prophesized reliability

N

Ratio of new test length to original test length

Arguments

Nlength

New length of a test in relation to original

rxx

reliability of test x

rxxp

reliability of desired (parallel) test x

Author

Thomas D. Fletcher

Details

Nlength represents a ratio of new to original. If the new test has 10 items, and the original test has 5 items, Nlength is 2. Likewise, if the original test has 5 items, and the new test has 10 items, Nlength is .5. In general, researchers should aim for reliabilities > .9.

SBrel is used to address the question, what if I increased/decreased my test length? What will the new reliability be? This is used when computing split-half reliabilities and when when concerned about reducing test length.
SBlength is used to address the question, how long must my test be (in relation to the original test) in order to achieve a desired reliability?
The formulae for each are:
rxxp <- Nlength*rxx/(1+(Nlength-1)*rxx)
N <- rxxp*(1-rxx)/(rxx*(1-rxxp))

References

Allen, M. J. & Yen, W. M. (1979). Introduction to measurement theory. Monterey, CA: Brooks/Cole.

See Also

alpha

Examples

# Given a test with rxx = .7, 10 items
# Desire a test with rxx=.9, how many items are needed?
new.length <- SBlength(.9, .7)
new.length * 10
# 39 items are needed
# what is the reliability of a test 1/2 as long
SBrel(.5, .7)