WINETASTER ON 02/07/00 WITH 8 JUDGES AND 6 WINES BASED ON RANKS, IDENT=N
Copyright (c) 1995-2000 Richard E. Quandt
FLIGHT 1:
Number of Judges = 8
Number of Wines = 6
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Troplong Mondot 1970 ........ 3rd place
Wine B is Ch. Lafite Rothschild 1966 ........ 1st place
Wine C is Ch. Brane Cantenac 1970 ........ 2nd place
Wine D is Ch. Troplong Mondot 1966 tied for 4th place
Wine E is Ch. Lafite Rothschild 1970 tied for 4th place
Wine F is Ch. Brane Cantenac 1966 ........ 6th place
The Judges's Rankings
Judge Wine -> A B C D E F
Burt 6. 4. 2. 5. 3. 1.
Frank 1. 4. 5. 2. 6. 3.
Bob 4. 1. 3. 6. 2. 5.
Ed 3. 4. 2. 1. 5. 6.
John 5. 6. 1. 3. 2. 4.
Grant 1. 2. 4. 3. 6. 5.
Orley 2. 1. 3. 4. 5. 6.
Dick 4. 2. 5. 6. 1. 3.
Table of Votes Against
Wine -> A B C D E F
Group Ranking -> 3 1 2 4 4 6
Votes Against -> 26 24 25 30 30 33
( 8 is the best possible, 48 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 = 0.0554
The probability that random chance could be responsible for this correlation
is rather large, 0.8188. 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
Orley 0.7714
Bob 0.1471
Grant 0.0857
Ed -0.0580
Dick -0.3769
John -0.4857
Frank -0.5798
Burt -0.6667
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 B is Ch. Lafite Rothschild 1966
2. ........ 2nd place Wine C is Ch. Brane Cantenac 1970
3. ........ 3rd place Wine A is Ch. Troplong Mondot 1970
4. tied for 4th place Wine D is Ch. Troplong Mondot 1966
5. tied for 4th place Wine E is Ch. Lafite Rothschild 1970
6. ........ 6th place Wine F is Ch. Brane Cantenac 1966
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 2.2143. The probability that this could
happen by chance is 0.8188
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
Burt Frank Bob
Burt 1.000 -0.600 0.086
Frank -0.600 1.000 -0.657
Bob 0.086 -0.657 1.000
Ed -0.543 0.314 -0.314
John 0.429 -0.543 -0.143
Grant -0.771 0.714 -0.029
Orley -0.600 0.200 0.486
Dick 0.257 -0.543 0.714
Ed John Grant
Burt -0.543 0.429 -0.771
Frank 0.314 -0.543 0.714
Bob -0.314 -0.143 -0.029
Ed 1.000 0.257 0.486
John 0.257 1.000 -0.657
Grant 0.486 -0.657 1.000
Orley 0.429 -0.486 0.829
Dick -0.829 -0.257 -0.371
Orley Dick
Burt -0.600 0.257
Frank 0.200 -0.543
Bob 0.486 0.714
Ed 0.429 -0.829
John -0.486 -0.257
Grant 0.829 -0.371
Orley 1.000 -0.086
Dick -0.086 1.000
Pairwise correlations in descending order
0.829 Grant and Orley Not significant
0.714 Bob and Dick Not significant
0.714 Frank and Grant Not significant
0.486 Bob and Orley Not significant
0.486 Ed and Grant Not significant
0.429 Ed and Orley Not significant
0.429 Burt and John Not significant
0.314 Frank and Ed Not significant
0.257 Burt and Dick Not significant
0.257 Ed and John Not significant
0.200 Frank and Orley Not significant
0.086 Burt and Bob Not significant
-0.029 Bob and Grant Not significant
-0.086 Orley and Dick Not significant
-0.143 Bob and John Not significant
-0.257 John and Dick Not significant
-0.314 Bob and Ed Not significant
-0.371 Grant and Dick Not significant
-0.486 John and Orley Not significant
-0.543 Burt and Ed Not significant
-0.543 Frank and Dick Not significant
-0.543 Frank and John Not significant
-0.600 Burt and Frank Not significant
-0.600 Burt and Orley Not significant
-0.657 John and Grant Not significant
-0.657 Frank and Bob Not significant
-0.771 Burt and Grant Not significant
-0.829 Ed and Dick Not significant
COMMENT:
The wines were lively and delicious; none of them is over the hill.
The Brane Cantenac 1970, first tasted in our group in 1989, was even
better today--despite its description by Robert Parker as 65 points, and
having a barnyard odor--and it had done well ten years ago.
One person said, "Apparently, Parker's ratings do not extend too far in
the future."
To show how dispersed preferences were, it should be noted that every wine
was rated best by at least one person, and every wine but one was rated
last by at least one person.
Conclusion: Many of us arrived at the tasting thinking that the wines
were probably going to be too old (one person said, "I want to go home"
when told what we were going to taste). In fact, the wines were delicious
today, very, very soft and quite delicious.
WINETASTER ON 02/07/00 WITH 8 JUDGES AND 2 WINES BASED ON RANKS, IDENT=Y
Copyright (c) 1995-2000 Richard E. Quandt
FLIGHT 2:
Number of Judges = 8
Number of Wines = 2
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Ducru Beaucaillou 1979 tied for 1st place
Wine B is Ch. Ducru Beaucaillou 1970 tied for 1st place
The Judges's Rankings
Judge Wine -> A B
Burt 2. 1.
Frank 2. 1.
Bob 2. 1.
Ed 1. 2.
John 1. 2.
Grant 1. 2.
Orley 1. 2.
Dick 2. 1.
Table of Votes Against
Wine -> A B
Group Ranking -> 1 1
Votes Against -> 12 12
( 8 is the best possible, 16 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 = 0.0000
The probability that random chance could be responsible for this correlation
is rather large, 1.0000. 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.
The correlation I measures the degree to which the identification of each
judge is correlated with the truth. Here a 1.0 means that the judge identified
the wines perfectly, and a 0 means that he identified none of them.
Correlation Between the Ranks of
Each Person With the Average Ranking of Others
Name of Person Correlation R Correlation I
Burt -1.0000 1.0000
Frank -1.0000 1.0000
Bob -1.0000 1.0000
Ed -1.0000 0.0000
John -1.0000 0.0000
Grant -1.0000 0.0000
Orley -1.0000 0.0000
Dick -1.0000 1.0000
Next, we show the correlation among the wine identifications of the judges,
which also ranges between 1.0 and 0.0:
C = 0.0000
The probability that random chance could be responsible for this correlation
is quite small: < 5 %. Most people would say that unless this probability
is less than 0.1, the judges' identifications are not highly related.
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. tied for 1st place Wine A is Ch. Ducru Beaucaillou 1979
2. tied for 1st place Wine B is Ch. Ducru Beaucaillou 1970
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 0.0000. The probability that this could
happen by chance is 1.0000
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 1.00 for significance at the 0.05
level and must exceed 1.00 for significance at the 0.1 level
Burt Frank Bob
Burt 1.000 1.000 1.000
Frank 1.000 1.000 1.000
Bob 1.000 1.000 1.000
Ed -1.000 -1.000 -1.000
John -1.000 -1.000 -1.000
Grant -1.000 -1.000 -1.000
Orley -1.000 -1.000 -1.000
Dick 1.000 1.000 1.000
Ed John Grant
Burt -1.000 -1.000 -1.000
Frank -1.000 -1.000 -1.000
Bob -1.000 -1.000 -1.000
Ed 1.000 1.000 1.000
John 1.000 1.000 1.000
Grant 1.000 1.000 1.000
Orley 1.000 1.000 1.000
Dick -1.000 -1.000 -1.000
Orley Dick
Burt -1.000 1.000
Frank -1.000 1.000
Bob -1.000 1.000
Ed 1.000 -1.000
John 1.000 -1.000
Grant 1.000 -1.000
Orley 1.000 -1.000
Dick -1.000 1.000
Pairwise correlations in descending order
1.000 Burt and Frank Significantly positive
1.000 Burt and Bob Significantly positive
1.000 John and Orley Significantly positive
1.000 Bob and Dick Significantly positive
1.000 Ed and John Significantly positive
1.000 Ed and Grant Significantly positive
1.000 Burt and Dick Significantly positive
1.000 Frank and Bob Significantly positive
1.000 John and Grant Significantly positive
1.000 Frank and Dick Significantly positive
1.000 Ed and Orley Significantly positive
1.000 Grant and Orley Significantly positive
-1.000 Burt and Ed Significantly negative
-1.000 Frank and Grant Significantly negative
-1.000 Bob and John Significantly negative
-1.000 Bob and Grant Significantly negative
-1.000 Bob and Orley Significantly negative
-1.000 Burt and John Significantly negative
-1.000 Burt and Grant Significantly negative
-1.000 Burt and Orley Significantly negative
-1.000 Bob and Ed Significantly negative
-1.000 Ed and Dick Significantly negative
-1.000 Frank and Ed Significantly negative
-1.000 Frank and John Significantly negative
-1.000 John and Dick Significantly negative
-1.000 Frank and Orley Significantly negative
-1.000 Grant and Dick Significantly negative
-1.000 Orley and Dick Significantly negative
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