Sample Size Again

"I notice that in the chapter on latent trait theory in the book Health Measurement Scales by D.L. Streiner and G.R. Norman (1995, New York: Oxford University Press), they argue that 200 subjects are required for the one parameter (Rasch) model when deriving an item characteristic curve. People will challenge my assertion that 50 cases will do! How shall I respond?"
Alan Tennant
Rheumatology and Rehabilitation Research Unit
University of Leeds, United Kingdom

An empirical item characteristic curve (ICC) plots the relationship between person ability (often represented by raw score) on the X-axis and proportion of success on the item on the Y-axis. It has the shape of a jagged line from lower left to upper right (see Rasch, 1992, pp. 71, 95 for many examples). For stable inference, however, this empirical shape must be superseded by an ideal form with clear properties. If the only constraint on the ICC were that increasing ability implies greater probability of success, then any ogive would suffice, e.g., arc tangent or 2- or 3-parameter models. When particular mathematical properties are required, however, then the relevant ogive is chosen. L. L. Thurstone conceptualized the tested sample as normally distributed and chose the cumulative normal ogive as his ICC.

Georg Rasch escaped from the awkward constraint that the sample be normally distributed by focussing on the requirement that the item parameters be separable from the person parameters. This leads to a logistic ogive for the ICC. Each item is now represented by one parameter which measures its difficulty relative to the other items. The logistic ICC is derived mathematically and its shape determined without reference to any data. In most cases, however, data is required to estimate each item's "one parameter" of difficulty. With a reasonably targeted sample of 50 persons, there is 99% confidence that the estimated item difficulty is within +-1 logit of its stable value - this is close enough for most practical purposes, especially when persons take 10 or more items. With 200 persons, there is 99% confidence the estimated value is within +-0.5 logits (see RMT 7:4 p. 328). But for pilot studies, 30 persons are enough to see what's happening (see Best Test Design). Even if you plan to test 200, start the analysis as soon as the first data become available: 200 incorrect administrations are never as good as 50 correct ones.

See Sample Size and Item Calibration (or Person Measure) Stability, Linacre JM. RMT, 1994, 7:4 p.328


Sample size again. Wright BD, Tennant A. … Rasch Measurement Transactions, 1996, 9:4 p.468



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
Rasch Books and Publications: Winsteps and Facets
Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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
Facets Tutorials - free
Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan

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