| ETL {betafunctions} | R Documentation |
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)
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). |
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
# 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)