WINETASTER ON 05/05/03 WITH 7 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2003 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 7 Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. du Pape, Marcoux, 1998 tied for 4th place Wine B is Ch. du Pape, Pegau, 1998 ........ 3rd place Wine C is Ch. du Pape, Le Vieux Donjon, 1998 tied for 1st place Wine D is Ch. du Pape, Cailloux, 1998 tied for 1st place Wine E is Ch. du Pape, Beaucastel, 1998 tied for 4th place Wine F is Ch. du Pape, Usseglio, 1998 ........ 6th place Wine G is Ch. du Pape, Beaurenard, 1998 ........ 7th place
The Judges's Rankings
Judge Wine -> A B C D E F G Bob 1. 2. 5. 3. 7. 4. 6. Ed 7. 6. 4. 2. 3. 1. 5. Burt 6. 5. 2. 1. 3. 4. 7. John 2. 3. 1. 6. 4. 5. 7. Frank 2. 1. 4. 5. 3. 6. 7. Orley 4. 3. 5. 2. 1. 6. 7. Dick 5. 4. 1. 3. 6. 2. 7.
Table of Votes Against Wine -> A B C D E F G
Group Ranking -> 4 3 1 1 4 6 7 Votes Against -> 27 24 22 22 27 28 46
( 7 is the best possible, 49 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 = 0.3017
The probability that random chance could be responsible for this correlation is quite small, 0.0485. 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 Dick 0.3424 0.0541 Burt 0.3273 -0.0360 John 0.2000 -0.3063 Orley 0.1786 -0.1802 Frank -0.0357 -0.3964 Bob -0.1429 0.1982 Ed -0.3455 0.3964
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. tied for 1st place Wine D is Ch. du Pape, Cailloux, 1998 2. tied for 1st place Wine C is Ch. du Pape, Le Vieux Donjon, 1998 3. ........ 3rd place Wine B is Ch. du Pape, Pegau, 1998 4. tied for 4th place Wine A is Ch. du Pape, Marcoux, 1998 5. tied for 4th place Wine E is Ch. du Pape, Beaucastel, 1998 6. ........ 6th place Wine F is Ch. du Pape, Usseglio, 1998 --------------------------------------------------- 7. ........ 7th place Wine G is Ch. du Pape, Beaurenard, 1998 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 12.6735. The probability that this could happen by chance is 0.0485
We now test whether the group ranking of wines is correlated with the prices of the wines. The rank correlation between them is -0.3945. At the 10% level of significance this would have to exceed the critical value of 0.5710 to be significant.
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 0.79 for significance at the 0.05 level and must exceed 0.71 for significance at the 0.1 level Bob Ed Burt Bob 1.000 -0.429 -0.143 Ed -0.429 1.000 0.643 Burt -0.143 0.643 1.000 John 0.321 -0.429 0.143 Frank 0.500 -0.571 0.000 Orley 0.071 0.071 0.536 Dick 0.250 0.429 0.643 John Frank Orley Bob 0.321 0.500 0.071 Ed -0.429 -0.571 0.071 Burt 0.143 0.000 0.536 John 1.000 0.714 0.179 Frank 0.714 1.000 0.607 Orley 0.179 0.607 1.000 Dick 0.429 0.000 -0.071 Dick Bob 0.250 Ed 0.429 Burt 0.643 John 0.429 Frank 0.000 Orley -0.071 Dick 1.000 Pairwise correlations in descending order 0.714 John and Frank Significantly positive 0.643 Ed and Burt Not significant 0.643 Burt and Dick Not significant 0.607 Frank and Orley Not significant 0.536 Burt and Orley Not significant 0.500 Bob and Frank Not significant 0.429 John and Dick Not significant 0.429 Ed and Dick Not significant 0.321 Bob and John Not significant 0.250 Bob and Dick Not significant 0.179 John and Orley Not significant 0.143 Burt and John Not significant 0.071 Bob and Orley Not significant 0.071 Ed and Orley Not significant 0.000 Burt and Frank Not significant 0.000 Frank and Dick Not significant -0.071 Orley and Dick Not significant -0.143 Bob and Burt Not significant -0.429 Bob and Ed Not significant -0.429 Ed and John Not significant -0.571 Ed and Frank Not significant
COMMENT: The standard of overall winemaking quality was very high. All the wines are very easy to drink now. It was absolutely widely agreed that one wine did not perform at the same level of quality of the others-- the Chateau Beaurenard 1998. These are warm wines with a sun-baked Mediterranean character with high alcohol. They are very food-friendly. There was a very high correlation within the group, but it should be noted that this was essentially driven by the almost total unanimity on the quality of wine G (Beaurenard). Omitting wine G, our rankings would have been essentially random.
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