Cumulative Probabilities

 

Select by clicking on "Cumulative Probabilities" or from the Graphs menu.

 

Lines: This shows the modeled category probability curves accumulated 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 the lowest or next lowest category. And so on to the right. If the categories are number 1, 2, 3, 4, 5. Then the red line is the probability of observing category 1. The blue line is the probability of observing categories 1 or 2. The pink line is the probability of observing categories 1 or 2 or 3. The black line is the probability of observing categories 1 or 2 or 3 or 4. The probability of observing categories 1 or 2 or 3 or 4 or 5 (which includes every category) is 1.0 and corresponds to the upper side of the graph box.

 

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-Thurstone thresholds. 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 red arrow points to the Thurstone threshold where the probability of observing category 1 and of observing categories 2 or 3 or 4 or 5 are equal. The is called the Thurstone threshold for Category 2. The blue arrow points to the Thurstone threshold where the probability of observing categories 1 or 2 and of observing categories 3 or 4 or 5 are equal. The is called the Thurstone threshold for Category 3. The interval between the Thurstone Threshold for Category 2 and the Thurstone Threshold for Category 3 is one definition of the interval for category 2 on the latent variable.

 

Buttons are described in Graph window.

 

Click on the "Flip Curves Vertically" button to change the vertical direction of the curves. This reverses the definition of the cumulative probability curves. When flipped the red line in the plot above is the probability of observing categories 2 or 3 or 4 or 5. The flipped blue line in the plot above is the probability of observing categories 3 or 4 or 5.  The flipped  pink line is the probability of observing categories 4 or 5. The black line is the probability of observing category 5. Flipping the curves does not change the Thurstone Thresholds. The red arrow continues to point to the Thurstone Threshold for category 2.

 


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Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
Winsteps Tutorials Facets Tutorials Rasch Discussion Groups

 


 

 
Coming Rasch-related Events
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
Jan. 22-24, 2018, Mon-Wed. In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx
April 10-12, 2018, Tues.-Thurs. Rasch Conference: IOMW, New York, NY, www.iomw.org
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 27 - 29, 2018, Wed.-Fri. Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 25 - July 27, 2018, Wed.-Fri. Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Sept. 3 - 6, 2018, Mon.-Thurs. IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

 

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