WINETASTER ON 02/03/03 WITH 8 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2003 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 8 Number of Wines = 8
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Leoville Las Cases 1989 ........ 2nd place Wine B is Ch. Ducru Beaucaillou 1970 ........ 5th place Wine C is Ch. Margaux 1976 ........ 7th place Wine D is Ch. Leoville Las Cases 1990 ........ 1st place Wine E is Ch. Latour 1993 ........ 6th place Wine F is Ch. Ducru Beaucaillou 1979 ........ 4th place Wine G is Ch. Latour 1977 ........ 8th place Wine H is Ch. Margaux 1989 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D E F G H Ed 3. 2. 5. 1. 4. 6. 8. 7. Bob 2. 1. 7. 5. 4. 6. 8. 3. Orley 1. 7. 6. 2. 5. 4. 8. 3. Burt 5. 6. 8. 1. 4. 2. 3. 7. John 1. 7. 4. 2. 6. 5. 8. 3. Grant 2. 4. 5. 1. 7. 6. 8. 3. Frank 1. 8. 7. 2. 4. 5. 6. 3. Dick 6. 3. 8. 2. 5. 1. 7. 4.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 2 5 7 1 6 4 8 3 Votes Against -> 21 38 50 16 39 35 56 33
( 8 is the best possible, 64 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 = 0.4628
The probability that random chance could be responsible for this correlation is quite small, 0.0005. 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 and with the Prices of the Wines
Name of Person Correlation R Correlation Price Orley 0.8743 0.4551 John 0.7904 0.3234 Grant 0.7381 0.6108 Frank 0.6587 0.3234 Dick 0.5030 0.6108 Ed 0.5000 0.9222 Bob 0.3810 0.6467 Burt 0.1905 0.3473
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 D is Ch. Leoville Las Cases 1990 2. ........ 2nd place Wine A is Ch. Leoville Las Cases 1989 --------------------------------------------------- 3. ........ 3rd place Wine H is Ch. Margaux 1989 4. ........ 4th place Wine F is Ch. Ducru Beaucaillou 1979 5. ........ 5th place Wine B is Ch. Ducru Beaucaillou 1970 6. ........ 6th place Wine E is Ch. Latour 1993 --------------------------------------------------- 7. ........ 7th place Wine C is Ch. Margaux 1976 8. ........ 8th place Wine G is Ch. Latour 1977 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 25.9167. The probability that this could happen by chance is 0.0005
We now test whether the group ranking of wines is correlated with the prices of the wines. The rank correlation between them is 0.6707. At the 10% level of significance this would have to exceed the critical value of 0.5240 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 0.74 for significance at the 0.05 level and must exceed 0.64 for significance at the 0.1 level Ed Bob Orley Ed 1.000 0.548 0.381 Bob 0.548 1.000 0.381 Orley 0.381 0.381 1.000 Burt 0.167 -0.286 0.190 John 0.381 0.286 0.929 Grant 0.643 0.548 0.762 Frank 0.214 0.238 0.905 Dick 0.333 0.310 0.333 Burt John Grant Ed 0.167 0.381 0.643 Bob -0.286 0.286 0.548 Orley 0.190 0.929 0.762 Burt 1.000 -0.048 -0.048 John -0.048 1.000 0.833 Grant -0.048 0.833 1.000 Frank 0.333 0.786 0.571 Dick 0.548 0.095 0.310 Frank Dick Ed 0.214 0.333 Bob 0.238 0.310 Orley 0.905 0.333 Burt 0.333 0.548 John 0.786 0.095 Grant 0.571 0.310 Frank 1.000 0.167 Dick 0.167 1.000 Pairwise correlations in descending order 0.929 Orley and John Significantly positive 0.905 Orley and Frank Significantly positive 0.833 John and Grant Significantly positive 0.786 John and Frank Significantly positive 0.762 Orley and Grant Significantly positive 0.643 Ed and Grant Not significant 0.571 Grant and Frank Not significant 0.548 Bob and Grant Not significant 0.548 Burt and Dick Not significant 0.548 Ed and Bob Not significant 0.381 Ed and Orley Not significant 0.381 Ed and John Not significant 0.381 Bob and Orley Not significant 0.333 Burt and Frank Not significant 0.333 Orley and Dick Not significant 0.333 Ed and Dick Not significant 0.310 Bob and Dick Not significant 0.310 Grant and Dick Not significant 0.286 Bob and John Not significant 0.238 Bob and Frank Not significant 0.214 Ed and Frank Not significant 0.190 Orley and Burt Not significant 0.167 Ed and Burt Not significant 0.167 Frank and Dick Not significant 0.095 John and Dick Not significant -0.048 Burt and John Not significant -0.048 Burt and Grant Not significant -0.286 Bob and Burt Not significant
COMMENT: During the tasting, the judges noted that all the wines were tasting wonderful and that it was very difficult to find differences among them. In the light of that, it is amazing that there was so much agreement among the judges; a concordance that was incredibly significant. The tasting is a testimonial of the vintage year. The top three rated wines from the group were in years 1989 and 1990, years with hot summers and little or insignificant autumn rain. The wine that we ranked last was from 1977, a year of a a quite cold summer, even tough it was a first growth. We were rather amazed at the correlation among the judges, because when we were tasting the, we thought that there was going to be no correlation among us. Independent of the tasting, Leoville just dominated the tasting.
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