Table 8 Scale structure probability curves

Use the "Graphs" pull down menu to obtain these as bit-mapped plots.

 

 

Specify "Graphfile=" to obtain the numbers to plot these yourself.

 

Table 8 includes a line-printer plot of the probability of occurrence for each category. The probability of the extreme categories always approaches 1.0 for corresponding extreme measures.

 

Most scale developers intend this to look like a series of hills, so that each category is in turn the most likely category along the latent variable.

 

Probability Curves

      -3.0       -2.0       -1.0        0.0        1.0        2.0        3.0

       ++----------+----------+----------+----------+----------+----------++

     1 |                                                                   |

       |                                                                   |

       |00                                                               22|

       |  00000                                                     22222  |

       |       000                                               222       |

     P |          000                                         222          |

     r |             00                                     22             |

     o |               00                                 22               |

     b |                 000                           222                 |

     a |                    00        1111111        22                    |

     b |                      0  11111       11111  2                      |

     i |                      1**                 **1                      |

     l |                   111   00             22   111                   |

     i |                 11        00         22        11                 |

     t |              111            00     22            111              |

     y |           111                 00*22                 111           |

       |       1111                    22 00                    1111       |

       |   1111                     222     000                     1111   |

       |111                    22222           00000                    111|

       |               22222222                     00000000               |

     0 |222222222222222                                     000000000000000|

       ++----------+----------+----------+----------+----------+----------++

      -3.0       -2.0       -1.0        0.0        1.0        2.0        3.0

 

The expected score ogive shows the average rating value expected for any measure relative to the item, judge etc. The ogive also indicates the category "zone", e.g., the area between average ratings of 0.5 and 1.5 is marked by 1's plotted on the curve.

 

Expected Score Ogive

      -2.0         -1.0          0.0          1.0          2.0          3.0

       ++------------+------------+------------+------------+------------++

     2 |                                                                  |

       |                                                            222222|

       |                                                     2222222      |

       |                                                22222             |

       |                                           22222                  |

       |                                        122                       |

       |                                    1111                          |

       |                                 111                              |

       |                               11                                 |

       |                            111                                   |

     1 |                         111                                      |

       |                      111                                         |

       |                    11                                            |

       |                 111                                              |

       |             1111                                                 |

       |          001                                                     |

       |     00000                                                        |

       |00000                                                             |

       |                                                                  |

       |                                                                  |

     0 |                                                                  |

       ++------------+------------+------------+------------+------------++

      -2.0         -1.0          0.0          1.0          2.0          3.0

 

Dichotomous plots always look the same:

 

Dichotomous scale structures are always the same:

 

Probability Curves for Dichotomies

     -2.0             -1.0              0.0              1.0              2.0

      ++----------------+----------------+----------------+----------------++

    1 |                                                                     |

      |                                                                     |

      |1                                                                   0|

      | 1111111                                                     0000000 |

      |        11111                                           00000        |

    P |             11111                                 00000             |

    r |                  1111                         0000                  |

    o |                      1111                 0000                      |

    b |                          111           000                          |

    a |                             1111   0000                             |

    b |                                 ***                                 |

    i |                             0000   1111                             |

    l |                          000           111                          |

    i |                      0000                 1111                      |

    t |                  0000                         1111                  |

    y |             00000                                 11111             |

      |        00000                                           11111        |

      | 0000000                                                     1111111 |

      |0                                                                   1|

      |                                                                     |

    0 |                                                                     |

      ++----------------+----------------+----------------+----------------++

     -2.0             -1.0              0.0              1.0              2.0

 

Expected Score Ogive (Model ICC)

     -2.0             -1.0              0.0              1.0              2.0

      ++----------------+----------------+----------------+----------------++

    0 |                                                                     |

      |                                                                     |

      |                                                               000000|

      |                                                        0000000      |

      |                                                  000000             |

      |                                             00000                   |

      |                                         0000                        |

      |                                     0000                            |

      |                                11000                                |

      |                            1111                                     |

      |                        1111                                         |

      |                   11111                                             |

      |             111111                                                  |

      |      1111111                                                        |

      |111111                                                               |

      |                                                                     |

    1 |                                                                     |

      ++----------------+----------------+----------------+----------------++

     -2.0             -1.0              0.0              1.0              2.0


Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
 

The Languages of Love: draw a map of yours!

For more information, contact info@winsteps.com or use the Contact Form
 

Facets Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download

State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied
 
Rasch, Winsteps, Facets online Tutorials

 

Forum Rasch Measurement Forum to discuss any Rasch-related topic

Click here to add your email address to the Winsteps and Facets email list for notifications.

Click here to ask a question or make a suggestion about Winsteps and Facets software.

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 Winsteps & Facets Events
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
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

Our current URL is www.winsteps.com

Winsteps® is a registered trademark
 

John "Mike" L.'s Wellness Report: I'm 72, take no medications and, March 2018, my doctor is annoyed with me - I'm too healthy!
According to Wikipedia, the human body requires about 30 minerals, maybe more. There are 60 naturally-occurring minerals in the liquid Mineral Supplement which I take daily.