Table 8 Scale structure bar-chart

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This gives several pictorial representations of the rating scale (or partial credit).

 

Scale structure for "FACES"

Measr:-3.0       -2.0       -1.0        0.0        1.0        2.0        3.0

       +          +          +          +          +          +          +

 Mode:<0---------(^)----------01--------^-------12-----------(^)---------2>

 

Median:<0---------(^)--------01----------^---------12---------(^)---------2>

 

 Mean:<0---------(^)------01------------^-----------12--------(^)--------2>

       +          +          +          +          +          +          +

Measr:-3.0       -2.0       -1.0        0.0        1.0        2.0        3.0

 

Mode: Most Probable Category

 

The values are relative to the relevant item difficulty.

The category labels are located at the measures where they commence to be the most probable observations. Omitted categories are never most probable. ^ indicates location of category peak probability. (^) indicates point at which extreme category becomes very probable.

Median: Rasch-Thurstone Threshold

 

The values are relative to the relevant item difficulty.

The category labels are located at the measures where there is the same probability (0.5) of being rated below that category as there is of being rated in that category or above. Conceptually, each category label is at the left-hand end of its "zone" on the variable. ^ indicate the mid-points of each zone. (^) indicates a conceptual mid-point of the infinitely long extreme zones.

Mean: Expected Score

 

The values are relative to the relevant item difficulty.

 

The mean values are usually more dispersed than the median, and the median than the mode.

The category labels are located at the measures where the expected values become closer to that score than the preceding score, i.e., at the half score-points. ^ indicates the locations where the category score is the expected score. (^) indicates the location at which the expected score is 0.25 score points away from the extreme category score.

the "mean" values below Table 8.2 (shown above) are the "scale" values on the right side of Table 6.0, and are the "Expectation" measures in Table 8.1. They answer the question: if we had 1,000 people at a particular measure relative to the item difficulty, what would we expect their average (mean) rating to be?

Measr: Measure relative to item difficulty

The scale of relative measures, e.g., persons relative to an item. The local origin is the mean of the Rasch-Andrich thresholds (step calibrations) or as determined by the anchored categories.

 

Dichotomous scale structures are always the same:

 

Scale structure for dichotomies

 

Measr:-2.0             -1.0              0.0              1.0              2.0

       +                +                +                +                +

 Mode:<0--------------------------------(^)--------------------------------0>

 

Median:<0--------------------------------(^)--------------------------------0>

 

 Mean:<0--------------------------------(^)--------------------------------0>

       +                +                +                +                +

Measr:-2.0             -1.0              0.0              1.0              2.0

 

 

 

Test


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Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn, 2024 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
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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
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