WINETASTER ON 11/05/07 WITH 7 JUDGES AND 9 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2007 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 7 Number of Wines = 9
Identification of the Wine: The judges' overall ranking:
Wine A is Vosne Romanee Les Chaumes Rion 1990 ........ 3rd place Wine B is Romanee Conti La Tache 1990 ........ 2nd place Wine C is Clos de la Roche Rousseau 1990 tied for 4th place Wine D is Le Chambertin Rousseau 1990 tied for 4th place Wine E is Clos Vougeot Gros F&S 1990 ........ 1st place Wine F is Nuits-St-Georges Gouges 1990 ........ 7th place Wine G is Clos Vougeot Jadot 1990 ........ 9th place Wine H is Chambertin Clos de Beze Faiveley 1990 ........ 8th place Wine I is Beaune Greves M. LaFarge 1990 ........ 6th place
The Judges's Rankings
Judge Wine -> A B C D E F G H I John 1. 4. 8. 9. 5. 6. 7. 3. 2. Ed 8. 9. 6. 7. 1. 2. 3. 4. 5. Mike 2. 1. 3. 4. 5. 7. 6. 8. 9. Bob 3. 1. 4. 2. 5. 7. 8. 9. 6. Greg 5. 6. 4. 2. 3. 9. 7. 8. 1. Burt 8. 3. 5. 2. 1. 6. 7. 4. 9. Frank 3. 2. 1. 5. 4. 7. 8. 9. 6.
Table of Votes Against Wine -> A B C D E F G H I
Group Ranking -> 3 2 4 4 1 7 9 8 6 Votes Against -> 30 26 31 31 24 44 46 45 38
( 7 is the best possible, 63 is the worst)
Here is a measure of the correlation in the preferences of the judges which ranges between 1.0 (perfect correlation) and 0.0 (no correlation):
W = 0.1939
The probability that random chance could be responsible for this correlation is rather large, 0.2099. Most analysts would say that unless this probability is less than 0.1, the judges' preferences are not strongly related. We now analyze how each taster's preferences are correlated with the group preference. A correlation of 1.0 means that the taster's preferences are a perfect predictor of the group's preferences. A 0.0 means no correlation, while a -1.0 means that the taster has the reverse ranking of the group. This is measured by the correlation R.
Correlation Between the Ranks of Each Person With the Average Ranking of Others
Name of Person Correlation R Correlation Price Bob 0.7280 -0.5776 Frank 0.7000 -0.3196 Mike 0.6219 -0.5235 Greg 0.2092 0.0723 Burt 0.1261 -0.4924 John -0.2259 -0.0065 Ed -0.6333 0.6228
The wines were preferred by the judges in the following order. When the preferences of the judges are strong enough to permit meaningful differentiation among the wines, they are separated by -------------------- and are judged to be significantly different.
1. ........ 1st place Wine E is Clos Vougeot Gros F&S 1990 2. ........ 2nd place Wine B is Romanee Conti La Tache 1990 3. ........ 3rd place Wine A is Vosne Romanee Les Chaumes Rion 1990 4. tied for 4th place Wine D is Le Chambertin Rousseau 1990 5. tied for 4th place Wine C is Clos de la Roche Rousseau 1990 6. ........ 6th place Wine I is Beaune Greves M. LaFarge 1990 7. ........ 7th place Wine F is Nuits-St-Georges Gouges 1990 8. ........ 8th place Wine H is Chambertin Clos de Beze Faiveley 1990 9. ........ 9th place Wine G is Clos Vougeot Jadot 1990 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 10.8571. The probability that this could happen by chance is 0.2099 We now undertake a more detailed examination of the pair-wise rank correla- tions that exist between pairs of judges. First, we present a table in which you can find the correlation for any pair of judges, by finding one of the names in the left hand margin and the other name on top of a column. A second table arranges these correlations in descending order and marks which is significantly positive significantly negative, or not significant. This may allow you to find clusters of judges whose rankings were particularly similar or particularly dissimilar. Pairwise Rank Correlations Correlations must exceed in absolute value 0.70 for significance at the 0.05 level and must exceed 0.60 for significance at the 0.1 level John Ed Mike John 1.000 -0.167 -0.133 Ed -0.167 1.000 -0.667 Mike -0.133 -0.667 1.000 Bob -0.100 -0.750 0.833 Greg -0.033 -0.233 0.067 Burt -0.450 0.083 0.317 Frank -0.067 -0.567 0.817 Bob Greg Burt John -0.100 -0.033 -0.450 Ed -0.750 -0.233 0.083 Mike 0.833 0.067 0.317 Bob 1.000 0.467 0.317 Greg 0.467 1.000 0.067 Burt 0.317 0.067 1.000 Frank 0.833 0.417 0.200 Frank John -0.067 Ed -0.567 Mike 0.817 Bob 0.833 Greg 0.417 Burt 0.200 Frank 1.000 Pairwise correlations in descending order 0.833 Bob and Frank Significantly positive 0.833 Mike and Bob Significantly positive 0.817 Mike and Frank Significantly positive 0.467 Bob and Greg Not significant 0.417 Greg and Frank Not significant 0.317 Mike and Burt Not significant 0.317 Bob and Burt Not significant 0.200 Burt and Frank Not significant 0.083 Ed and Burt Not significant 0.067 Mike and Greg Not significant 0.067 Greg and Burt Not significant -0.033 John and Greg Not significant -0.067 John and Frank Not significant -0.100 John and Bob Not significant -0.133 John and Mike Not significant -0.167 John and Ed Not significant -0.233 Ed and Greg Not significant -0.450 John and Burt Not significant -0.567 Ed and Frank Not significant -0.667 Ed and Mike Significantly negative -0.750 Ed and Bob Significantly negative
COMMENT: A remarkable tasting of 1990 Burgundies! It is noteworthy that no wine stood out as significantly better than any other and that only one taster had a substantial correlation between his rankings and the prices of the wines.
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