Raw Scores Are Not Linear Measures: : Rasch vs. Classical Test Theory CTT Comparison
StandingRaw ScoresLinear Measures
Psychometrics Classical Test Theory CTT Rasch Model RM
Data must be "complete" robust against missing data and non-administered items
Meaning ordinal ranking on hoped-for latent variable linear positioning on latent variable explicitly-defined by item content
Status mistaken for truth known as estimates
Additivity non-linear, bent linear, straight
Continuity discrete, lumpy continuous, smooth
Precision unknown, except on average quantified by standard errors
Accuracy unknown quantified by local fit statistics
Linear Analysis unsuited to usual statistics ideal for usual statistics
Validity sample-dependent test "reliability" item-dependent construct validity
Diagnosis sample-dependent item point-biserial individual item and person fit statistics
Conceptualization concrete abstract
Occurrence accidental deliberate
Construction irreproducible reproducible
Scope local general
Relationships incomparable comparable
Context test-bound test-free
Integration awkward to equate simple to equate
Benjamin D. Wright

Raw Scores Are Not Linear Measures: : Rasch vs. Classical Test Theory CTT Comparison. B.D. Wright … Rasch Measurement Transactions, 1992, 6:1, 208

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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