﻿ Fair averages based on = Mean

# Fair averages based on = Mean

Fair average scores are reported in the output for each element. These are the scores that correspond to the logit measures as though each element of that facet encountered elements of similar difficulty in the other facets. Fair averages are intended for communicating the measures as adjusted ratings. This is useful when the audience have a strong conceptualization of the rating scale, but little interest in, or understanding of, the measurement system.

Fair score = Mean

This provides a norm-referenced average the measures for all elements (except this element) are set to the average values of the elements in their facets. It uses mean measure of the elements of each facet (except the current element) as the reference for computation. This is the default option. It is shown as Fair(M) in Table 7.

Fair score = Zero

This provides a criterion-referenced average the measures for all elements (except this element) are set to zero (logits or on user-scaling). It uses the origin of the measurement scale for each facet (except the current element) as the reference for computation. This was the default option in early version of Facets. It is shown as Fair(Z) in Table 7.

For the non-centered facet (typically persons), these two fair averages are usually the same. For a centered facet (e.g., items or raters) they are different. So for your non-centered rater facet, do you want the "fair-average" for a rater to be the rating given by this rater to a person with an "average" measure, or to a person with a "zero" measure? You may need to try both to identify which is actually what you want to report.

Look at your non-centered facet. Do you want the fair averages for all elements to be determined by a person at the Umean= value (Fair=zero)  or a person at the person-sample mean (Fair=mean).  If you are describing performances on this test then (fair=mean).

Example 1: An examination board wishes to use criterion-referenced fair scores for rater comparisons, because a "zero" logit person is at the pass-fail point:

Fair score = Zero

Example 2: An examination board wishes to use ratings based on an average task rated by an average rater:

Fair score = Mean

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

 Forum Rasch Measurement Forum to discuss any Rasch-related topic

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