WINETASTER ON 11/23/98 WITH 6 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N
Copyright (c) 1995-98 Richard E. Quandt
FLIGHT 1:
Number of Judges = 6
Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is Bandol-Tempier 1986 La Migoua tied for 2nd place
Wine B is Bandol-Tempier 1992 tied for 4th place
Wine C is Bandol-Tempier 1975 ........ 1st place
Wine D is Bandol-Tempier 1987 La Tourtine tied for 6th place
Wine E is Bandol-Tempier 1986 La Tourtine tied for 6th place
Wine F is Bandol-Tempier 1989 La Tourtine tied for 4th place
Wine G is Bandol-Tempier 1978 tied for 2nd place
The Judges's Rankings
Judge Wine -> A B C D E F G
Grant 2. 5. 1. 3. 6. 7. 4.
Frank 4. 3. 5. 6. 7. 2. 1.
Burt 6. 5. 2. 7. 4. 1. 3.
Orley 4. 3. 1. 2. 5. 6. 7.
John 1. 3. 2. 7. 4. 5. 6.
Dick 6. 7. 1. 4. 3. 5. 2.
Table of Votes Against
Wine -> A B C D E F G
Group Ranking -> 2 4 1 6 6 4 2
Votes Against -> 23 26 12 29 29 26 23
( 6 is the best possible, 42 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 = 0.2024
The probability that random chance could be responsible for this correlation
is rather large, 0.2952. 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
Grant 0.1818
John -0.0360
Burt -0.0541
Dick -0.0541
Orley -0.0714
Frank -0.2728
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 Bandol-Tempier 1975
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2. tied for 2nd place Wine A is Bandol-Tempier 1986 La Migoua
3. tied for 2nd place Wine G is Bandol-Tempier 1978
4. tied for 4th place Wine B is Bandol-Tempier 1992
5. tied for 4th place Wine F is Bandol-Tempier 1989 La Tourtine
6. tied for 6th place Wine E is Bandol-Tempier 1986 La Tourtine
7. tied for 6th place Wine D is Bandol-Tempier 1987 La Tourtine
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 7.2857. The probability that this could
happen by chance is 0.2952
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 Frank Burt
Grant 1.000 -0.214 -0.321
Frank -0.214 1.000 0.429
Burt -0.321 0.429 1.000
Orley 0.643 -0.571 -0.357
John 0.393 -0.107 0.036
Dick 0.321 -0.179 0.429
Orley John Dick
Grant 0.643 0.393 0.321
Frank -0.571 -0.107 -0.179
Burt -0.357 0.036 0.429
Orley 1.000 0.321 0.036
John 0.321 1.000 -0.214
Dick 0.036 -0.214 1.000
Pairwise correlations in descending order
0.643 Grant and Orley Not significant
0.429 Burt and Dick Not significant
0.429 Frank and Burt Not significant
0.393 Grant and John Not significant
0.321 Orley and John Not significant
0.321 Grant and Dick Not significant
0.036 Burt and John Not significant
0.036 Orley and Dick Not significant
-0.107 Frank and John Not significant
-0.179 Frank and Dick Not significant
-0.214 Grant and Frank Not significant
-0.214 John and Dick Not significant
-0.321 Grant and Burt Not significant
-0.357 Burt and Orley Not significant
-0.571 Frank and Orley Not significant
COMMENT:
Very fruity wines, remind you of Chateauneuf du Pape; half the group
thought they were nicer than Chateauneuf du Pape, half did not. Almost
everyone thought that the 1975 was a particularly good example, but the
wines were universally delicious. Burt says they were good, not delicious.
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