A Standard Setting Exercise

Longford (1996) poses an interesting problem in standard setting. 17 writing performances were randomly selected from all scored performances. They had ratings in the range 4-12. These 17 writers were each assessed as pass or fail by each of 16 experts. Now, what is the minimum rating for a pass?

-------------------------------------------------------------------
|         Expert's Classification of Writers: 1=Pass, 0=Fail      |
|-----------------------------------------------------------------|
|Writer: | 6 10 14  1  4  5  9 11 13 15 12  8 16  7 17  2  3|     |
|--------+--------------------------------------------------+-----|
|Rating: |10 12  9  8 11  8  7 11  6  8 10  9  6  6  7  4  5|Total|
|--------+--------------------------------------------------+-----|
|Expert 6| 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0|  16 |
|    2   | 1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  0|  15 |
|   11   | 1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0|  15 |
|   12   | 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0|  15 |
|    5   | 1  1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|  13 |
|    7   | 1  1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|  13 |
|    9   | 1  1  1  1  1  1  1  1  1  1  1  1  1  0  0  0  0|  13 |
|   14   | 1  1  1  0  1  1  1  1  1  0  1  1  1  1  1  0  0|  13 |
|   16   | 1  1  1  1  0  1  1  1  0  1  1  1  1  1  1  0  0|  13 |
|    1   | 1  1  1  1  0  1  1  1  1  1  0  1  1  1  0  0  0|  12 |
|    4   | 1  1  1  1  1  1  1  1  0  1  0  0  0  1  1  0  0|  11 |
|   15   | 1  1  1  1  1  0  1  0  1  1  0  1  0  1  1  0  0|  11 |
|    3   | 1  1  0  1  1  1  1  1  1  0  1  0  0  0  0  0  0|   9 |
|    8   | 1  1  1  0  0  1  0  1  1  0  1  0  1  0  1  0  0|   9 |
|   10   | 1  1  1  1  1  0  0  0  1  1  1  1  0  0  0  0  0|   9 |
|   13   | 1  0  1  1  1  0  0  0  0  1  0  0  0  0  0  0  1|   6 |
|--------+--------------------------------------------------+-----|
|Total   |16 15 15 14 13 13 13 13 13 13 12 11 11  9  8  3  1|  193|
-------------------------------------------------------------------

A routine Rasch analysis of Longford's data (shown Guttman-sorted in the Table) reveals that some data editing is needed. Expert 13 is the most severe and yet was the only expert to pass Writer 3 (the `1' in the bottom right corner of the data matrix). This causes Expert 13 to have large misfit statistics and a negative correlation with the other experts. He is not part of any consensus. The pass verdicts for Writer 17 also correlate negatively with the judges' perspectives of the other writers. This idiosyncratic Writer is also not part of any consensus. Once these irregular rating patterns are removed, consensus appears. Writer 3 is failed by everyone. Writers 6 and 10 are passed by everyone. In a second Rasch analysis, the writers are measured, establishing a frame of reference within which to identify the pass-fail criterion. In a third analysis, all writers are anchored at their measures from the second analysis (including Bayesian estimates for writers with extreme scores). Then measures are obtained for all experts, so that all (except 13) participate in setting the mean pass-fail point.

Writer's ratings vs. pass-fail measures are plotted in the Figure. The experts' severity measures are across the bottom of the plot. An expert of average severity would be expected to pass all performances to the right of the Y-axis. Also shown, for reference only, are Expert (13) and Examinee (17). We see that the bulk of the experts would be expected to pass papers rated 6 or more.

This plot also warns that the original ratings themselves are dubious. Writer 13, with a rating of 6, was deemed a more certain pass by these experts than Writer 4 with a rating of 11. The standard setting process could also be improved. Rather than selecting papers at random, focus on ratings near the expected pass-fail point using a stratified random sample. A better sampling plan would eliminate most of the papers rated 9-12, and select papers rated 4-7.

John Michael Linacre

Longford NT (1996) Reconciling experts' differences in setting cut scores for pass-fail decisions. Journal of Educational Statistics 21:3 203-213.

A standard setting exercise. Linacre J.M. … Rasch Measurement Transactions, 1996, 10:3 p. 521.

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	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
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
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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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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