Meaning by Norm?

"The first score that an examiner encounters is the raw score, which is simply a total of points earned on a single sub-test. The raw score by itself is meaningless because it is not norm referenced. ... Because intellectual ability in the general population is distributed on a normal curve, ... "

Kaufman A.S. & Lichtenberger E.O. (2000) Essential of WISC-III and WPPSI-R Assessment. New York: John Wiley & Sons. p. 64-65

How do we know intellectual ability is normally distributed? Because WISC scaled scores are normally distributed. Why are WISC scores normally distributed? Because intellectual ability is normally distributed! So what is the actual distribution of intellectual ability? Norm referencing will never tell us; we need a distribution-independent yardstick.

Let me norm-reference Emma's raw score. She is at the 86th percentile rank. OK - she's smart. But what can she think about? What would challenge her? She's also at the 86th percentile rank in shoes. OK - she's got big feet. But what size shoes does she need? Norm referencing is a commentary on the measures, not the meaning of the measures. The WISC-III needs to produce measures that have meaning even if Emma is the only one to take the instrument. This requires it to produce linear, criterion-referenced measures.

Meaning by Norm? Kaufman, A.S., Licthenbeger, E.O. … Rasch Measurement Transactions, 1999, 13:3 p. 708

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez

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