The reliability coefficient and the standard error of
measurement in classical test theory are not properties
of a specific test, but are attributed to both a specific
test and a specific trait distribution. In latent trait models,
or item response theory, the test information function
(TIF) provides more precise local measures of
accuracy in trait estimation than are available from the
reliability coefficient. The reliability coefficient is still
widely used, however, and is popular because of its
simplicity. Thus, it is worthwhile to relate it to the TIF.
In this paper, the reliability coefficient is predicted
from the TIF, or two modified TIF formulas, and a specific
trait distribution. Examples demonstrate the variability
of the reliability coefficient across different trait
distributions, and the results are compared with empirical
reliability coefficients. Practical suggestions are
given as to how to make better use of the reliability
coefficient. Index terms: adaptive testing, bias, classical
test theory, item information function, latent trait
models, maximum likelihood estimation, reliability coefficient,
standard error of measurement, test information
function, trait estimation.
Samejima, Fumiko. (1994). Estimation of reliability coefficients using the test information function and its modifications. Applied Psychological Measurement, 18, 229-244. doi:10.1177/014662169401800304
Estimation of reliability coefficients using the test information function and its modifications.
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