WINETASTER ON 03/02/09 WITH 6 JUDGES AND 6 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2009 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 6 Number of Wines = 6
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Lafite Rothschild 1996 ........ 4th place Wine B is Ch. Haut Brion 1997 tied for 1st place Wine C is Ch. Lafite Rothschild 1997 ........ 6th place Wine D is Ch. Margaux 1996 ........ 3rd place Wine E is Ch. Margaux 1997 tied for 1st place Wine F is Ch. Haut Brion 1996 ........ 5th place
The Judges's Rankings
Judge Wine -> A B C D E F Mike 6. 5. 3. 1. 2. 4. Orley 6. 1. 5. 2. 3. 4. Burt 2. 3. 6. 5. 1. 4. Bob 2. 3. 6. 5. 1. 4. Ed 3. 1. 4. 2. 5. 6. Dick 1. 2. 6. 4. 3. 5.
Table of Votes Against Wine -> A B C D E F
Group Ranking -> 4 1 6 3 1 5 Votes Against -> 20 15 30 19 15 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 = 0.3079
The probability that random chance could be responsible for this correlation is quite small, 0.0999. 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 Dick 0.6000 Bob 0.4928 Burt 0.4928 Orley 0.2899 Ed 0.2899 Mike -0.2571
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. The "Parker points" for each wine are given in parentheses at the end of each line.
1. tied for 1st place Wine B is Ch. Haut Brion 1997 (89) 2. tied for 1st place Wine E is Ch. Margaux 1997 (90) 3. ........ 3rd place Wine D is Ch. Margaux 1996 (99) 4. ........ 4th place Wine A is Ch. Lafite Rothschild 1996 (100) 5. ........ 5th place Wine F is Ch. Haut Brion 1996 (92) --------------------------------------------------- 6. ........ 6th place Wine C is Ch. Lafite Rothschild 1997 (92) We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 9.2381. The probability that this could happen by chance is 0.0999 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 Mike Orley Burt Mike 1.000 0.371 -0.314 Orley 0.371 1.000 0.029 Burt -0.314 0.029 1.000 Bob -0.314 0.029 1.000 Ed -0.143 0.486 -0.086 Dick -0.543 0.086 0.771 Bob Ed Dick Mike -0.314 -0.143 -0.543 Orley 0.029 0.486 0.086 Burt 1.000 -0.086 0.771 Bob 1.000 -0.086 0.771 Ed -0.086 1.000 0.486 Dick 0.771 0.486 1.000 Pairwise correlations in descending order 1.000 Burt and Bob Significantly positive 0.771 Bob and Dick Not significant 0.771 Burt and Dick Not significant 0.486 Orley and Ed Not significant 0.486 Ed and Dick Not significant 0.371 Mike and Orley Not significant 0.086 Orley and Dick Not significant 0.029 Orley and Burt Not significant 0.029 Orley and Bob Not significant -0.086 Burt and Ed Not significant -0.086 Bob and Ed Not significant -0.143 Mike and Ed Not significant -0.314 Mike and Burt Not significant -0.314 Mike and Bob Not significant -0.543 Mike and Dick Not significant
COMMENT: All the wines were truly delicious. All were in perfect condition. These wines have passed their tenth anniversary and are absolutely drinkable now, with ripe fruit and good acidity. Our host wisely provided a comparison of two vintages and three chateaux of first growth Bordeaux chateau wines. Margaux was the top wine in the tasting. Haut Brion was second and Lafite third. The 1997s slightly edged out the 1996s. The 1997 Margaux and Haut Brion were tied. On a price adjusted basis, 1997 is clearly the more attractive vintage to buy. It is interesting to note that the rank correlation (adjusted for ties) between the group's ranking of the wines and the Parker rankings is -0.382; hence a not inconsequential disagreement exists between the group and the Parker ratings.
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