WINETASTER ON 05/03/99 WITH 5 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N
Copyright (c) 1995-99 Richard E. Quandt
FLIGHT 1:
Number of Judges = 5
Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Cheval Blanc 1990 ........ 2nd place
Wine B is Ch. Leoville Barton 1990 ........ 7th place
Wine C is Ch. Haut Brion 1990 tied for 3rd place
Wine D is Ch. Meyney 1990 tied for 3rd place
Wine E is Ch. Lafite Rothschild 1990 ........ 5th place
Wine F is Ch. Bourgneuf 1990 ........ 6th place
Wine G is Ch. Margaux 1990 ........ 1st place
The Judges's Rankings
Judge Wine -> A B C D E F G
Grant 1. 2. 7. 3. 6. 5. 4.
John 5. 7. 4. 6. 2. 1. 3.
Burt 6. 7. 1. 2. 5. 4. 3.
Bob 3. 4. 7. 2. 5. 6. 1.
Dick 4. 5. 1. 7. 3. 6. 2.
Table of Votes Against
Wine -> A B C D E F G
Group Ranking -> 2 7 3 3 5 6 1
Votes Against -> 19 25 20 20 21 22 13
( 5 is the best possible, 35 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 = 0.1143
The probability that random chance could be responsible for this correlation
is rather large, 0.7534. 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 -0.0371
Dick -0.1429
Burt -0.3706
John -0.4144
Grant -0.7207
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. Margaux 1990
2. ........ 2nd place Wine A is Ch. Cheval Blanc 1990
3. tied for 3rd place Wine C is Ch. Haut Brion 1990
4. tied for 3rd place Wine D is Ch. Meyney 1990
5. ........ 5th place Wine E is Ch. Lafite Rothschild 1990
6. ........ 6th place Wine F is Ch. Bourgneuf 1990
7. ........ 7th place Wine B is Ch. Leoville Barton 1990
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 3.4286. The probability that this could
happen by chance is 0.7534
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
Grant John Burt
Grant 1.000 -0.643 -0.607
John -0.643 1.000 0.214
Burt -0.607 0.214 1.000
Bob 0.643 -0.357 -0.107
Dick -0.500 0.250 0.250
Bob Dick
Grant 0.643 -0.500
John -0.357 0.250
Burt -0.107 0.250
Bob 1.000 -0.214
Dick -0.214 1.000
Pairwise correlations in descending order
0.643 Grant and Bob Not significant
0.250 John and Dick Not significant
0.250 Burt and Dick Not significant
0.214 John and Burt Not significant
-0.107 Burt and Bob Not significant
-0.214 Bob and Dick Not significant
-0.357 John and Bob Not significant
-0.500 Grant and Dick Not significant
-0.607 Grant and Burt Not significant
-0.643 Grant and John Not significant
COMMENT:
This was an extraordinarily wonderful wine tasting and the lack of
agreement indicates that these were all wonderful wines and 1990 is a
wonderful vintage, says Burt. Bob adds athat he agrees with Burt, these
are amazing wines, perhaps the best of the century. Differentiation is
more noise than anything else. John says that these wines were all so good
that the dispersion is unusually high, as expected. Grant says that the
wines have great fruit.
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