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 a score on the normal distribution (with a mean 0 and a standard deviation of 1) to a score on a 0-500 scale or a 0-300 scale as indicated below. For more information on the ranges for final subject area score scales, see NAEP frameworks for each subject area.
|Subject||Score scale range|
|Mathematics, grades 4 and 8||0–500|
|Mathematics, grade 12||0–300|
|SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP).|