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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).
Last updated 17 June 2008 (KL)