NAEP Technical DocumentationTransformation Constants for NAEP Assessments

To transform the score estimates that are obtained from the IRT scaling program to the NAEP reporting metric, two transformation constants, A and B, are calculated and then used in a linear transformation equation. The transformation equation is as follows:

θ_target = A• θ_calibrated+B

where θ_target denotes scale score values on the final transformed scale and θ_calibrated denotes values on the original calibration scale from the BILOG/PARSCALE IRT scaling program. When the NAEP scales for geography, mathematics, reading, and U.S. history were first created, A values were close to 50, and B values were close to 250. In subsequent assessment years, the A and B values have varied, and separate transformations have been calculated for each grade level. The A and B transformation constants have been calculated for each link depicted in the linking diagrams.

For the 2004 long-term trend assessment, two sets of transformation constants were needed in order to maintain trend. In 1999, scale scores on the trend line were obtained. The 2004 bridge assessment was identical to the 1999 assessment, and accommodations were offered in neither assessment. As a result, the standard NAEP linking procedure (common calibration) was utilized. Linking transformation constants (A1 and B1) for the set of 1999 samples (i.e., original results from the 1999 assessment and the re-estimated results from the bridge assessment) were calculated to place the two sets of results onto the same scale (i.e., set the means and standard deviations equal across the two sets of results). These same transformation constants were then applied to the 2004 bridge plausible values, creating 2004 bridge scale scores that are on the trend line.

In order to link the 2004 modified assessment to the 2004 bridge assessment, equivalent population design was used. In the case of the modified assessment, accommodations were offered, but there were no accommodations offered in the bridge assessment. Therefore, the non-SD/ELL portions of both the bridge and modified samples were theoretically randomly equivalent samples. Plausible values were obtained for the modified sample using a single-sample calibration. The subset of non-SD/ELL students of the modified sample (from these plausible values) was used to calculate the linking transformation constants (A2 and B2) to the non-SD/ELL subset of scale scores obtained for the bridge sample. These linking transformation constants were then applied to all students in the modified sample, thus creating 2004 modified scale scores that are linked to the existing trend line.

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