Cumulative probabilities (Rasch-Thurstonian thresholds) |
Select by clicking on "Cumulative Thresholds" in the Graphs window.
Lines: This shows the modeled category probability curves accumulated in pairs so that the left-hand curve (red) is the probability of being observed in the lowest category. The next curve (blue) is the probability of being observed in categories above the lowest category. Then the next curve (brown) is the probability of being observed in the two lowest categories. The next curve (pink) is the probability of being observed in categories above the two lowest categories. And so on to the right for rating scales with more categories.
The cumulative probability is the y-axis in this graph, but is the x-axis in G.N. Masters (1988) "The Analysis of Partial Credit Scoring" (Figure 2), Applied Measurement in Education, 1:4, 279-297. The cumulative probability accumulates the probabilities across the categories upwards from low category to high category (or vice versa) for any ability level.
Arrows: The points of intersection between these curves and the 0.5 probability line are the Rasch-Thurstonian thresholds (green arrows). The points at which being observed in this category (or below) and the category above (or higher) are equal. These curves are always in the order of the category scores. The interval between the Thurstonian Threshold for Category 2 and the Thurstonian Threshold for Category 3 is one definition of the interval for category 2 on the latent variable.
Buttons are described in Graph window.
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Coming Rasch-related Events | |
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May 17 - June 21, 2024, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
June 12 - 14, 2024, Wed.-Fri. | 1st Scandinavian Applied Measurement Conference, Kristianstad University, Kristianstad, Sweden http://www.hkr.se/samc2024 |
June 21 - July 19, 2024, Fri.-Fri. | On-line workshop: Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com |
Aug. 5 - Aug. 7, 2024, Mon.-Wed. | 2024 Inaugural Conference of the Society for the Study of Measurement (Berkeley, CA), Call for Proposals |
Aug. 9 - Sept. 6, 2024, Fri.-Fri. | On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com |
Oct. 4 - Nov. 8, 2024, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
Jan. 17 - Feb. 21, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
May 16 - June 20, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
June 20 - July 18, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Further Topics (E. Smith, Facets), www.statistics.com |
Oct. 3 - Nov. 7, 2025, Fri.-Fri. | On-line workshop: Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com |
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