7 facet Paired comparison with ties: Flavor Strength of Gels
In order to determine the effect of varying gel and flavor concentration on the subjective evaluation of flavor strength, assessors were asked to state which sample of each pair had the greater flavor strength. A decision of "no difference" was allowed. The data is from A. Springall (Applied Statistics, 22/1, p. 66). This analysis models the comparison as a three category rating scale: 2 = prefer first sample, 1 = tie, 0 = prefer second sample. Enter each datapoint twice in your data: A vs. B and B vs. A. Model weighting is 0.5 to adjust for this.
Note: If a rater facet is used to identify the judge, then anchor the rater elements at 0. Their fit statistics will characterize their behavior relative to the consensus.
Facets specifications and data (in file Gel.txt):
title = Gel Comparison Rating Scale ; report heading
facets = 7 ;7 facets in data set up for several analyses
positive = 1,2,3,4 ; measure everything in the same direction
non-center = 1 ; allow for skew in data due to arbitrary selection of "first" and "second" samples
entry = 1,4,4,2,3,2,3 ; several pairs in the comparisons
;X,?, X,?,?, X, X,Stronger,1.0 ; to check the raw scores
?, , ,?,?,-?,-?,Stronger,0.5 ; for the components
;?,?,-?,X,X, X, X,Stronger,0.5 ; for the treatments - commented out this time
Rating (or partial credit) scale = Stronger,R2
2 = Prefer first ; the possible outcomes
1 = Tie
0 = Prefer second
1,Centering ; adjusts for lack of symmetry in choice of origin
1=Offset ; since Facets 2 & 3 are anchored so that there is
; a clear meaning to the 0 of the scale,
; this element, named "Offset" is specified for every
; observation and allowed to float.
2=Flavor,A ; anchoring for the local origin
1=0.6,0 ; choose origin for convenience in comprehension
3=Gel,A ; anchoring for local origin
1=0.0,0 ; choose origin for convenience in comprehension
4=Treatment ; ignored for main analysis
1= 0.6 0.0 ; name reflects flavor-gel combination
2= 4.8 0.0
9= 9.0 4.8
data = ;885 comparisons in total (entered twice, weighted 0.5)
; count, offset, 1st treatment, 2nd treatment, 1st flavor, 1st gel, 2nd flavor, 2nd gel, preference
R2,1 ,2,1, 2,1, 1,1, 0 ; 1st treatment 4.8/0.0 compared with 2nd treatment 0.6/0.0, 2nd preferred
R8,1 ,9,8, 3,3, 2,3, 2 ; last recorded comparison
; data entered again in reverse sequence
R2,1 ,1,2, 1,1, 2,1, 2 ; 1st treatment 0.6/0.0 compared with 2nd treatment 4.9/0.0, 1st preferred
R8,1 ,8,9, 2,3, 3,3, 0 ; last recorded comparison - reversed
Anchoring flavor strength of "0.6" at 0 logits, and gel strength "0.0" at 0 logits, gives the measurement system a substantive zero, similar to zero on the Celsius temperature measurement system. Since both flavor and gel facets are anchored, we introduce another facet, "Centering" and its element, "Offset", which compensates for the misalignment between flavor and gel.
Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
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|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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