WINETASTER ON 5/2/1996 WITH 7 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2011 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 Ch. Gruaud Larose 1975 ........ 7th place Wine B is Ch. Talbot 1975 ........ 6th place Wine C is Ch. Talbot 1982 tied for 2nd place Wine D is Ch. Gruaud Larose 1982 ........ 5th place Wine E is Ch. Talbot 1983 ........ 8th place Wine F is Ch. Gruaud Larose 1983 tied for 2nd place Wine G is Ch. Gruaud Larose 1979 ........ 1st place Wine H is Ch. Talbot 1979 tied for 2nd place
The Judges's Rankings
Judge Wine -> A B C D E F G H Dick 5. 1. 8. 7. 4. 6. 3. 2. Ed 5. 4. 3. 1. 6. 2. 7. 8. Ken 4. 8. 3. 6. 7. 5. 1. 2. Dave 6. 7. 1. 4. 5. 2. 3. 8. John 2. 1. 3. 4. 8. 7. 6. 5. Orley 8. 7. 5. 6. 4. 3. 2. 1. Frank 7. 8. 5. 4. 6. 3. 1. 2.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 7 6 2 5 8 2 1 2 Votes Against -> 37 36 28 32 40 28 23 28
( 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 = 0.1127
The probability that random chance could be responsible for this correlation is rather large, 0.5963. 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 Frank 0.6946 Ken 0.5904 Orley 0.4192 Dave 0.2036 Ed -0.2515 Dick -0.4910 John -0.5868
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 G is Ch. Gruaud Larose 1979 2. tied for 2nd place Wine F is Ch. Gruaud Larose 1983 3. tied for 2nd place Wine C is Ch. Talbot 1982 4. tied for 2nd place Wine H is Ch. Talbot 1979 5. ........ 5th place Wine D is Ch. Gruaud Larose 1982 6. ........ 6th place Wine B is Ch. Talbot 1975 7. ........ 7th place Wine A is Ch. Gruaud Larose 1975 8. ........ 8th place Wine E is Ch. Talbot 1983 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 5.5238. The probability that this could happen by chance is 0.5963 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 Dick Ed Ken Dick 1.000 -0.690 -0.071 Ed -0.690 1.000 -0.476 Ken -0.071 -0.476 1.000 Dave -0.762 0.524 0.214 John 0.071 0.214 -0.143 Orley 0.214 -0.500 0.571 Frank -0.048 -0.262 0.738 Dave John Orley Dick -0.762 0.071 0.214 Ed 0.524 0.214 -0.500 Ken 0.214 -0.143 0.571 Dave 1.000 -0.286 0.095 John -0.286 1.000 -0.714 Orley 0.095 -0.714 1.000 Frank 0.286 -0.571 0.857 Frank Dick -0.048 Ed -0.262 Ken 0.738 Dave 0.286 John -0.571 Orley 0.857 Frank 1.000 Pairwise correlations in descending order 0.857 Orley and Frank Significantly positive 0.738 Ken and Frank Significantly positive 0.571 Ken and Orley Not significant 0.524 Ed and Dave Not significant 0.286 Dave and Frank Not significant 0.214 Ken and Dave Not significant 0.214 Ed and John Not significant 0.214 Dick and Orley Not significant 0.095 Dave and Orley Not significant 0.071 Dick and John Not significant -0.048 Dick and Frank Not significant -0.071 Dick and Ken Not significant -0.143 Ken and John Not significant -0.262 Ed and Frank Not significant -0.286 Dave and John Not significant -0.476 Ed and Ken Not significant -0.500 Ed and Orley Not significant -0.571 John and Frank Not significant -0.690 Dick and Ed Significantly negative -0.714 John and Orley Significantly negative -0.762 Dick and Dave Significantly negative
COMMENT: The agreement in the group was poor, but it is still interesting to ask whether, on the whole, the Gruaud Larose wines were liked more or less than the Talbots. Both of these wines are St. Juliens. The upshot is that they were, and the difference in rank sums just misses being significant by a hair.
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