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
models =
;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
*
Labels =
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
2=4.8
3=9.0
*
3=Gel,A ; anchoring for local origin
1=0.0,0 ; choose origin for convenience in comprehension
2=2.4
3=4.8
*
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.