betafunctions (version 1.9.0)

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, min = 0, max = 1, reliability)

Value

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

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).

reliability

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

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))

# 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), min = 0, max = 100,
reliability = .7)