betafunctions (version 1.4.0)

ETL: Livingston and Lewis' "Effective Test Length".

Description

According to Livingston and Lewis (1995), "The effective test length corresponding to a test score is the number of discrete, dichotomously scored, locally independent, equally difficult items required to produce a total score of the same reliability."

Usage

ETL(mean, variance, l = 0, u = 1, reliability)

Arguments

mean

The mean of the observed-score distribution.

variance

The variance of the observed-score distribution.

l

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

u

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

reliability

The reliability of the observed scores (proportion of observed-score distribution variance shared with true-score distribution).

Value

An estimate of the effective length of a test, given the stability of the observations it produces.

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

# NOT RUN {
# 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))

# Suppose the reliability of this test was estimated to 0.7. To estimate and
# retrieve the effective test length using ETL():
ETL(mean = mean(testdata), variance = var(testdata), l = 0, u = 100,
reliability = .7)
# }