WINETASTER ON 01/07/02 WITH 6 JUDGES AND 6 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2002 Richard E. Quandt
FLIGHT 1: Number of Judges = 6 Number of Wines = 6
Identification of the Wine: The judges' overall ranking:
Wine A is Monpertuis 1990 tied for 3rd place Wine B is Bois de Boursan 1989 ........ 1st place Wine C is Boisdauphin 1990 ........ 2nd place Wine D is Lucien Barrot 1990 tied for 3rd place Wine E is Bousquet de Papes 1990 ........ 6th place Wine F is La Bernardine 1990 ........ 5th place
The Judges's Rankings
Judge Wine -> A B C D E F Grant 1. 3. 4. 5. 6. 2. Burt 6. 1. 3. 2. 5. 4. Orley 4. 1. 2. 3. 5. 6. Bob 3. 1. 6. 4. 2. 5. John 1. 4. 2. 3. 5. 6. Dick 5. 2. 1. 3. 6. 4.
Table of Votes Against Wine -> A B C D E F
Group Ranking -> 3 1 2 3 6 5 Votes Against -> 20 12 18 20 29 27
( 6 is the best possible, 36 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 = 0.3048
The probability that random chance could be responsible for this correlation is rather large, 0.1035. 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 Orley 0.8407 Dick 0.4414 John 0.4286 Burt 0.3714 Bob 0.0286 Grant -0.0857
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 B is Bois de Boursan 1989 --------------------------------------------------- 2. ........ 2nd place Wine C is Boisdauphin 1990 3. tied for 3rd place Wine A is Monpertuis 1990 4. tied for 3rd place Wine D is Lucien Barrot 1990 5. ........ 5th place Wine F is La Bernardine 1990 --------------------------------------------------- 6. ........ 6th place Wine E is Bousquet de Papes 1990 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 9.1429. The probability that this could happen by chance is 0.1035 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 0.89 for significance at the 0.05 level and must exceed 0.83 for significance at the 0.1 level Grant Burt Orley Grant 1.000 -0.257 -0.086 Burt -0.257 1.000 0.714 Orley -0.086 0.714 1.000 Bob -0.086 0.086 0.200 John 0.257 -0.143 0.486 Dick 0.029 0.771 0.771 Bob John Dick Grant -0.086 0.257 0.029 Burt 0.086 -0.143 0.771 Orley 0.200 0.486 0.771 Bob 1.000 -0.143 -0.371 John -0.143 1.000 0.257 Dick -0.371 0.257 1.000 Pairwise correlations in descending order 0.771 Burt and Dick Not significant 0.771 Orley and Dick Not significant 0.714 Burt and Orley Not significant 0.486 Orley and John Not significant 0.257 John and Dick Not significant 0.257 Grant and John Not significant 0.200 Orley and Bob Not significant 0.086 Burt and Bob Not significant 0.029 Grant and Dick Not significant -0.086 Grant and Bob Not significant -0.086 Grant and Orley Not significant -0.143 Burt and John Not significant -0.143 Bob and John Not significant -0.257 Grant and Burt Not significant -0.371 Bob and Dick Not significant
COMMENT: According one taster, the Lucien Barrot was distinctly different from the other wines: it was a more interesting wine. General comments: 1. We all agreed that the wines are mature and ready to drink and nothing is over the hill. 2. We consumed them with sausages and firm cheeses and the combination was irresistible. 3. The wines that were the winners were the ones that were smoother and sweeter. 4. There is no tannin left in these wines at all.
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