betafunctions (version 1.9.0)

R.ETL: Model Implied Reliability from Livingston and Lewis' "Effective Test Length".

Description

Calculate model-implied reliability given mean, variance, the minimum and maximum possible scores, and the effective test length.

Usage

R.ETL(mean, variance, min = 0, max = 1, ETL)

Value

An estimate of the reliability of a test, given the effective test length, mean, variance, and minimum and maximum possible scores of the observed-score distribution..

Arguments

mean

The mean of the observed-score distribution.

variance

The variance of the observed-score distribution.

min

The lower-bound (minimum possible value) of the observed-score distribution. Default is 0 (assuming observed scores represent proportions).

max

The upper-bound (maximum possible value) of the observed-score distribution. Default is 1 (assuming observed scores represent proportions).

ETL

The effective test length as defined by Livingston and Lewis (1995).

References

Livingston, Samuel A. and Lewis, Charles. (1995). Estimating the Consistency and Accuracy of Classifications Based on Test Scores. Journal of Educational Measurement, 32(2).

Examples

# Generate some fictional data. Say, 100 individuals take a test with a
# maximum score of 100 and a minimum score of 0.
set.seed(1234)
testdata <- rbinom(100, 100, rBeta.4P(100, .25, .75, 5, 3))
hist(testdata, xlim = c(0, 100))

# From the data-generating script above, the effective test length is 100.
# To estimate and retrieve the model-implied reliability using R.ETL():
R.ETL(mean = mean(testdata), variance = var(testdata), min = 0, max = 100,
ETL = 100)