Cross-Language Test Equating

How can performance levels in different languages be compared? Here are the steps we used to equate four tests, each developed to measure one of four skills (vocabulary, analogies, reading and writing) in one language (English), to four similar tests in a second language (Spanish) for the Woodcock-Muñoz Language Surveys (Chicago: Riverside, 1993).

Step 1. Develop a bank of English items for each of the four skill areas.

Step 2. Rasch analyze the responses of subjects (6,359, ages 2 to 95) to establish the scale underlying each of the four banks of English items. Discard misfitting items.

Step 3. Compute norm measure tables of typical English language performance at different educational levels, ages, etc.

Step 4. Select sets of items for the four published English tests from their respective banks. Compute a raw score-to- measure table for each test for field use.

Step 5. Identify a subset of items covering the full difficulty range from "easy" to "difficult" in each English test and translate into Spanish. Verify that each English item has a reasonably direct counterpart in Spanish, e.g., authority/autoridad. (Though translated from English items of known difficulty, the difficulty of the Spanish items is still unknown.)

Step 6. Develop item banks for the four Spanish tests. Imbed in each bank of Spanish items the set of equating items translated from English.

Step 7. Rasch analyze the responses of Spanish speakers from outside the USA (1,200) and Spanish speakers from within the USA (800, pre-school to university graduate). Establish item difficulties for each Spanish item bank.

Step 8. Plot the English and Spanish difficulties for equivalent items for each skill area. Do not expect perfect agreement between the two sets of calibrations, because there are language-related differences for specific item content. Evaluate outliers from the best fit line for exclusion from the set of equating items. (This step verifies success in constructing comparable English- and Spanish-language variables.)

Step 9. Select items for the published versions of the Spanish tests. Compute a raw score-to-Spanish measure table for each test.

Step 10. Compute means (Me for English and Ms for Spanish) and standard deviations (Se for English and Ss for Spanish) of the English and Spanish equating item calibrations for each pair of tests.

Step 11. Equate each Spanish measure, Bs, to the scale of English measures, with value Be, by


Step 12. Construct a raw score to English equated measure table for each Spanish test, so that an examiner using the Spanish tests on native Spanish-speaking subjects can use the English equated measures to identify in the English language norm tables the typical performance levels for native English speakers of equivalent language competency.

Richard W. Woodcock
Ana Muñoz-Sandoval

Cross-Language Test Equating. Woodcock R., Muñoz-Sandoval A. Rasch Measurement Transactions 1994 7:4 p.329


Rasch publications in Spanish - Español
www.rasch.org/rmt/glosario.htmRasch Anàlisis - Glosario Español - Spanish Glossary - Español-Inglés del diccionario - Spanish-English Dictionary - Dr. Agustín Tristàn Lòpez
www.rasch.org/diseno.htmSpanish language introduction to Diseño de Mejores Pruebas (Best Test Design)
Book PDFDiseño de Mejores Pruebas - Spanish-language translation of Best Test Design (Wright & Stone, 1979)

Cross-Language Test Equating. Woodcock R., Muñoz-Sandoval A. … Rasch Measurement Transactions, 1994, 7:4 p.329



Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse Rasch Measurement Theory Analysis in R, Wind, Hua Applying the Rasch Model in Social Sciences Using R, Lamprianou El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Rasch Models for Measurement, David Andrich Constructing Measures, Mark Wilson Best Test Design - free, Wright & Stone
Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias Diseño de Mejores Pruebas - free, Spanish Best Test Design A Course in Rasch Measurement Theory, Andrich, Marais Rasch Models in Health, Christensen, Kreiner, Mesba Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen
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Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang Statistical Analyses for Language Testers (Facets), Rita Green Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind Rasch Measurement: Applications, Khine Winsteps Tutorials - free
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Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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