Noisy Responding and Intervention Effectiveness

The Rasch model is widely used for test development and item functioning. Noisy individuals are often a major concern because they distort item estimates, weakening inferences based on item difficulties. A typical practice is to omit and disregard individuals who are not constructive for item calibration purposes. But application of the Rasch model and information from misfitting participants can assist the evaluation of interventions in research on individuals. By examining misfitting participants useful information can be extracted regarding the strengths and weaknesses of an intervention or the specific behaviors of the individuals involved.

Figure 1. Tracy's fluency as a function of goal setting and reinforcement. Values above horizontal lines indicate Tracy achieved the goal for the session.

Figure 1 shows data from Tracy who was subjected to a "goal setting and reinforcement" intervention in order to improve her fluency. Using a changing criterion design, Tracy was asked to reach one goal after another and was reinforced contingently on her performance. The difficulty of the material was increased over sessions. As shown in Figure 1, Tracy reached some of the goals and missed some other, suggesting that the proposed intervention was not all that effective for her.

Using 5 students for comparative purposes I fit a Rasch model to the data of the 6 students by coding student's behavior during a session as 1 (if a student met the goal for that session) or 0 (if the student missed the goal). Given that difficulty increased in every session we can hypothesize that student's behavior could fit the Rasch model (e.g., 1 1 1 1 1 0 1 0 1 0 0 0) for this particular research design. The presence of large fit statistics would suggest a pattern of responding that deviates from the Rasch model, or, in other words, that the intervention has not been as effective as hypothesized. An exception would be a one category responding (e.g., all 1s) which would still indicate that the student behaved contrary to expectations (as if the activity was too easy for the student).

Table 1 shows out-fit mean-square and point-measure correlations for all students, suggesting that Tracy's responding was not in accord to expectations, in comparison to her peers (see also Figure 2).

Raw Score	Measure	Outfit Mean-square	Point-measure correlation	Student
9 8 8 6 6 6	1.30 0.83 0.83 0.02 0.02 0.02	1.54 0.60 0.88 0.68 0.89 1.58	0.12 0.67 0.39 0.68 0.51 -0.07	John Lex Bill Mike Steve Tracy

Table 1. Evaluation of students' response patterns.

Tracy's response pattern, 010101000111, is erratic, but provides useful information regarding her capabilities and her unique reaction to the intervention. She was able to reach some of the most challenging goals, but missed goals of medium and easy difficulty. She may fit the profile of an overachiever who got bored during some of the sessions or a student with attention problems, low motivation, etc. Alternatively, the intervention can be evaluated by examining, refining, and developing the content of the sessions in which Tracy failed, if there is room to improve the content of the test.

Figure 2. Erratic performance by Tracy and John.

By focusing on a student's noisy performance, researchers in psychology and education may gain greater understanding of both student behaviors and intervention effectiveness. This knowledge base may assist them in developing effective educational interventions and in remediating learning difficulties.

Georgios, D. Sideridis
Department of Psychology, University of Crete

Noisy Responding and Intervention Effectiveness. Sideridis, G.D. … Rasch Measurement Transactions, 2005, 19:2 p. 1013-4

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
Other 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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