WINETASTER ON 01/05/09 WITH 7 JUDGES AND 8 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 = 8
Identification of the Wine: The judges' overall ranking:
Wine A is Corton, Bouchard,1999 ........ 2nd place Wine B is Clos des Cortons, Faiveley,2002 ........ 7th place Wine C is Corton Renardes, Girardin, 1998 ........ 1st place Wine D is Corton Bressandes, Prieur,2003 ........ 6th place Wine E is Corton Grancey, Latour, 1993 ........ 4th place Wine F is Clos des Cortons, Faiveley, 2001 ........ 8th place Wine G is Corton Bressandes, Briailles, 2002 ........ 5th place Wine H is Corton Bressandes, Briailles, 2003 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D E F G H Alexa 3. 6. 1. 8. 5. 7. 4. 2. Ed 6. 7. 4. 2. 1. 8. 3. 5. Burt 1. 6. 4. 2. 5. 8. 3. 7. Mike 1. 5. 2. 4. 8. 6. 3. 7. Bob 5. 7. 1. 6. 4. 8. 3. 2. John 3. 2. 6. 5. 4. 8. 7. 1. Dick 4. 7. 3. 5. 1. 6. 8. 2.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 2 7 1 6 4 8 5 3 Votes Against -> 23 40 21 32 28 51 31 26
( 7 is the best possible, 56 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 = 0.3294
The probability that random chance could be responsible for this correlation is quite small, 0.0238. 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 Bob 0.6467 Alexa 0.6266 Ed 0.2874 Burt 0.2857 Dick 0.2635 John 0.0359 Mike 0.0241
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 C is Corton Renardes, Girardin, 1998 2. ........ 2nd place Wine A is Corton, Bouchard,1999 3. ........ 3rd place Wine H is Corton Bressandes, Briailles, 2003 4. ........ 4th place Wine E is Corton Grancey, Latour, 1993 5. ........ 5th place Wine G is Corton Bressandes, Briailles, 2002 6. ........ 6th place Wine D is Corton Bressandes, Prieur,2003 7. ........ 7th place Wine B is Clos des Cortons, Faiveley,2002 --------------------------------------------------- 8. ........ 8th place Wine F is Clos des Cortons, Faiveley, 2001 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 16.1429. The probability that this could happen by chance is 0.0238 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 0.74 for significance at the 0.05 level and must exceed 0.64 for significance at the 0.1 level Alexa Ed Burt Alexa 1.000 0.024 0.095 Ed 0.024 1.000 0.452 Burt 0.095 0.452 1.000 Mike 0.310 -0.119 0.738 Bob 0.857 0.476 0.190 John 0.262 -0.048 -0.024 Dick 0.429 0.381 -0.071 Mike Bob John Alexa 0.310 0.857 0.262 Ed -0.119 0.476 -0.048 Burt 0.738 0.190 -0.024 Mike 1.000 0.167 -0.214 Bob 0.167 1.000 0.143 John -0.214 0.143 1.000 Dick -0.357 0.476 0.405 Dick Alexa 0.429 Ed 0.381 Burt -0.071 Mike -0.357 Bob 0.476 John 0.405 Dick 1.000 Pairwise correlations in descending order 0.857 Alexa and Bob Significantly positive 0.738 Burt and Mike Significantly positive 0.476 Bob and Dick Not significant 0.476 Ed and Bob Not significant 0.452 Ed and Burt Not significant 0.429 Alexa and Dick Not significant 0.405 John and Dick Not significant 0.381 Ed and Dick Not significant 0.310 Alexa and Mike Not significant 0.262 Alexa and John Not significant 0.190 Burt and Bob Not significant 0.167 Mike and Bob Not significant 0.143 Bob and John Not significant 0.095 Alexa and Burt Not significant 0.024 Alexa and Ed Not significant -0.024 Burt and John Not significant -0.048 Ed and John Not significant -0.071 Burt and Dick Not significant -0.119 Ed and Mike Not significant -0.214 Mike and John Not significant -0.357 Mike and Dick Not significant
COMMENT: If we had had any of these wines at a good restaurant, we would have been pleased , except for wine F. It is interesting to note that the older wines did better than the others, in that the 1993, 1998, and 1999 had average scores of 24, which is much better than the others. In fact, we can perform the appropriate significance test for the null hypothesis that the older wines are equal to the younger ones, using the test suggested in Quandt, R. E., "A Note on a Test for the Sum of Ranksums," Journal of Wine Economics, May 2007, pp. 98-102. The test statistic in the present case is 0.6667, whereas the critical value at the 0.05 level is 0.7651; hence the result emphatically rejects the null hypothesis. It is also interesting to note that the Faiveley wines were the least liked. Despite the fact that this tasting spanned 10 years and 7 producers, it illustrated that there is a Corton style. None of these wines despite their differences deviated from that. There is a question about their design for the long haul. The interested reader may wish to compare this tasting to another Corton tasting that took place almost one year earlier, which is reported in Report 118.
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