Table of Contents  |  Search Technical Documentation  |  References

NAEP Analysis and Scaling → Scale Linking and Transformation to the Reporting Metric → The Transformation Equation

NAEP Technical DocumentationThe Transformation Equation

NAEP uses transformations of the form

where

θtarget	=	scale level in terms of the system of units of the final scale used for reporting,
θcalibrated	=	scale level in terms of the system of units of the provisional NAEP BILOG/PARSCALE scale centered around zero,
A	=	SDtarget /SDcalibrated ,
B	=	Mtarget – A × Mcalibrated ,
SDtarget	=	the estimated or selected standard deviation of the scale score distribution to be matched,
SDcalibrated	=	the estimated standard deviation of the sample scale score distribution on the provisional NAEP BILOG/PARSCALE scale,
Mtarget	=	the estimated or selected mean of the scale score distribution to be matched, and
Mcalibrated	=	the estimated mean of the sample scale score distribution on the provisional NAEP BILOG/PARSCALE scale.

After the provisional NAEP BILOG/PARSCALE scale scores are linearly transformed to the new scale, any plausible value less than 0 is censored to 0. For all subjects, any plausible value less than 0 is censored to 0 and, depending on the subject, the upper limit is censored to either 300 (e.g. science) or 500 (e.g. mathematics).

Printer-friendly Version