Close examination of the two-parameter logistic, three-parameter logistic, and generalized partial credit models indicates that the models have a linear indeterminacy of the score scale. In other words, if the item parameters are estimated in a different metric, the score scale could be transformed to make the equations describing the models true. For the purposes of reporting item parameter estimates and other intermediary estimates, the linear indeterminacies may be resolved by an arbitrary choice of the origin and unit size in a given scale. In most cases, a provisional scale standardizing the score scale distribution to have mean 0 and standard deviation 1 is employed. Final results for each subject area are transformed from either a 0, 1 scale to a 0-to-500 or a 0-to-300 scale as indicated below.
|Subject||Score scale range|
|Mathematics, grades 4 and 8||0–500|
|Mathematics, grade 12||0–300|
|Mathematics, long-term trend||0–500|
|Reading, long-term trend||0–500|
|SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2000-2008.|