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 For stable inference, however, this empirical shape must be superseded by an ideal form with clear properties.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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