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)
www.rasch.org/spanish.htmDiseño de Mejores Pruebas - Spanish-language book of Best Test Design (Wright & Stone, 1979)

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

Please help with Standard Dataset 4: Andrich Rating Scale Model



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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