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 lefthand 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 yaxis in this graph, but is the xaxis in G.N. Masters (1988) "The Analysis of Partial Credit Scoring" (Figure 2), Applied Measurement in Education, 1:4, 279297. 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 RaschThurstone 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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Coming Raschrelated Events  

Jan. 5  Feb. 2, 2018, Fri.Fri.  Online workshop: Practical Rasch Measurement  Core Topics (E. Smith, Winsteps), www.statistics.com 
Jan. 1016, 2018, Wed.Tues.  Inperson workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement 
Jan. 1719, 2018, Wed.Fri.  Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website 
Jan. 2224, 2018, MonWed.  Inperson workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx 
April 1012, 2018, Tues.Thurs.  Rasch Conference: IOMW, New York, NY, www.iomw.org 
April 1317, 2018, Fri.Tues.  AERA, New York, NY, www.aera.net 
May 22  24, 2018, Tues.Thur.  EALTA 2018 preconference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank WeissMotz), https://ealta2018.testdaf.de 
May 25  June 22, 2018, Fri.Fri.  Online 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.  Online workshop: Practical Rasch Measurement  Further Topics (E. Smith, Winsteps), www.statistics.com 
July 25  July 27, 2018, Wed.Fri.  PacificRim Objective Measurement Symposium (PROMS), (Preconference workshops July 2324, 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.  Online workshop: ManyFacet 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.  Online workshop: Practical Rasch Measurement  Core Topics (E. Smith, Winsteps), www.statistics.com 
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