On the Assessment of Gain Scores by Means of Item Response Theory Gerhard H. Fischer Abstract
The problem of the
measurement and statistical assessment of change based on test scores
which arises in repeated measurement designs with two time points is
treated within an item response theory framework. The latter is
delineated by postulating a Partial Credit Model, of which the Rating
Scale Model and the Rasch Model are special cases. A conditional
maximum likelihood estimator of the amount of change, Clopper-Pearson
and related significance tests for the change parameter, uniformly
most accurate confidence intervals, and uniformly most powerful
unbiased tests are presented. They are all 'exact' in the sense that
no asymptotic approximations are needed. They are grounded on the
conditional distribution of the gain score, given the sum score of
both time points. These methods are quite flexible because they do
not require the same test to be given on both occasions; it is
necessary, though, that the items presented at the two time points be
chosen from an item pool conforming to the Partial Credit Model, and
that the item |