Table 2.2 Mean observed categories (average or expected categories: Rasch-half-point thresholds )

(controlled by T2SELECT=, MRANGE=, CATREF=)

 

EXPECTED SCORE: MEAN  (Rasch-score-point threshold, ":" indicates Rasch-half-point threshold) (ILLUSTRATED BY AN OBSERVED CATEGORY)

-5   -4    -3    -2    -1     0     1     2     3     4     5

|-----+-----+-----+-----+-----+-----+-----+-----+-----+-----|  NUM   TAP

0                                                   0      :1   15  1-3-2-4-1-3

0                                                   0      :1   16  1-4-2-3-1-4

0                                                   0      :1   17  1-4-3-1-2-4

|                                                           |

|                                                           |

0                                           0     :      1  1   14  1-4-2-3-4-1

|                                                           |

0                                    0     :      1         1   12  1-3-2-4-3

0                                  0      :     1           1   13  1-4-3-2-4

|                                                           |

0                           0      :     1                  1   11  1-3-1-2-4

|                                                           |

|                                                           |

0             0      :     1                                1   10  2-4-3-1

|                                                           |

0        0      :     1                                     1    8  1-4-2-3

|                                                           |

0  0      :     1                                           1    6  3-4-1

0  0      :     1                                           1    9  1-3-2-4

0      :      1                                             1    5  2-1-4

0      :      1                                             1    7  1-4-3-2

0   :     1                                                 1    4  1-3-4

|-----+-----+-----+-----+-----+-----+-----+-----+-----+-----|  NUM   TAP

-5   -4    -3    -2    -1     0     1     2     3     4     5

 

                            1

1   1   2   2    2    3     2       5     4    1    2          KID

 T            S             M            S            T

0      10       20   30    60      80    90        99          PERCENTILE

 

Table 2.2 is used for inference:

 

Past-sample-dependent inference: If you expect the future person to be from a person sample exactly like the past sample (distribution, ability level, misfit, etc.) , then base your decisions on Table 2.7.

 

Past-sample-distribution-dependent inference: If you expect the future person to be from a person sample similar to the past sample (distribution, ability level, but not misfit) , then base your decisions on Table 2.5.

 

Past-sample-independent-as-possible: If you have no information about the future person, except that the latent variable will be the same as for the past sample, then base your decisions on Table 2.2.

 

Does the future repeat the past? Or is the future something entirely new? The truth is usually somewhere between these extremes.

 

Multiple-choice items

 

Table 2.2: shows the predicted average response on the latent variable. In this example, for item "al07", "a" (or any other incorrect option) is the predicted average response up to 3.2 logits, then "d", the correct response, becomes the average predictions. The ":" is at the transition from an average expected wrong response to an average expected "right" response, i.e., where the predicted average score on the item is 0.5, the Rasch-half-point thresholds. The "a" below "2" is positions where the expected average score on the item is 0.25. Similarly "d" would be repeated where the expected average score on the item is 0.75, according to the Rasch model.

 

TABLE 2.2 EXPECTED SCORE: MEAN  (":" INDICATES HALF-POINT THRESHOLD) (ILLUSTRATED BY AN OBSERVED CATEGORY)

-4    -3     -2     -1      0      1      2      3      4

|------+------+------+------+------+------+------+------|  NUM   TOPIC

a                                          a       :    d   55  al07  newspaper

a                                         a       :     c   64  sa01  magazine

 

Table 2.12 is the same as Table 2, but the options are shown by their scored values, not by their codes in the data.

 

TABLE 2.12 EXPECTED SCORE: MEAN  (":" INDICATES HALF-POINT THRESHOLD) (BY CATEGORY SCORE)

-4    -3     -2     -1      0      1      2      3      4

|------+------+------+------+------+------+------+------|  NUM   TOPIC

0                                          0       :    1   55  al07  newspaper

0                                         0       :     1   64  sa01  magazine

 


 

Polytomous items

 

Tables 2.2 & 2.12: In the "Expected Score" Table, the standard output (or selected with CURVES=010) answers the question "what is the average rating that we expect to observer for persons of a particular measure?" This rating information is expressed in terms of expected scores (with ":" at the half-point thresholds). Extreme scores are located at expected scores .25 score points away from the extremes. This plot also indicates the operational range of each item.

 

In this example of a 5 category rating scale, the operation range of the top item is indicated in red.

 

-5       -3        -1         1         3         5         7

|---------+---------+---------+---------+---------+---------|  NUM   ITEM

1                        1  :   2  : 3 :  4    :   5        5   13  M. STAIRS

      Operational range: ^-------------------------^

|---------+---------+---------+---------+---------+---------|  NUM   ITEM

-5       -3        -1         1         3         5         7


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

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 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

 

 

Our current URL is www.winsteps.com

Winsteps® is a registered trademark
 


 
Concerned about aches, pains, youthfulness? Mike and Jenny suggest Liquid Biocell