WINETASTER ON 02/15/99 WITH 7 JUDGES AND 4 WINES BASED ON RANKS, IDENT=N
Copyright (c) 1995-98 Richard E. Quandt
FLIGHT 1:
Number of Judges = 7
Number of Wines = 4
Identification of the Wine: The judges' overall ranking:
Wine A is Lenz 1988 ........ 1st place
Wine B is Sassicaia 1988 ........ 2nd place
Wine C is Ch. Palmer 1988 ........ 4th place
Wine D is Ch. Cheval Blanc 1988 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D
Ed 1. 2. 3. 4.
Burt 3. 1. 2. 4.
Grant 1. 3. 4. 2.
Orley 2. 1. 4. 3.
John 2. 3. 4. 1.
Frank 2. 1. 3. 4.
Dick 3. 4. 1. 2.
Table of Votes Against
Wine -> A B C D
Group Ranking -> 1 2 4 3
Votes Against -> 14 15 21 20
( 7 is the best possible, 28 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 = 0.1510
The probability that random chance could be responsible for this correlation
is rather large, 0.3659. 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
Ed 0.7379
Orley 0.7379
Frank 0.6000
Burt 0.0000
Grant 0.0000
John -0.3162
Dick -0.9487
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 A is Lenz 1988
2. ........ 2nd place Wine B is Sassicaia 1988
3. ........ 3rd place Wine D is Ch. Cheval Blanc 1988
4. ........ 4th place Wine C is Ch. Palmer 1988
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 3.1714. The probability that this could
happen by chance is 0.3659
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
Ed Burt Grant
Ed 1.000 0.400 0.400
Burt 0.400 1.000 -0.600
Grant 0.400 -0.600 1.000
Orley 0.600 0.400 0.400
John -0.200 -0.800 0.800
Frank 0.800 0.800 0.000
Dick -0.600 -0.400 -0.400
Orley John Frank
Ed 0.600 -0.200 0.800
Burt 0.400 -0.800 0.800
Grant 0.400 0.800 0.000
Orley 1.000 0.200 0.800
John 0.200 1.000 -0.400
Frank 0.800 -0.400 1.000
Dick -1.000 -0.200 -0.800
Dick
Ed -0.600
Burt -0.400
Grant -0.400
Orley -1.000
John -0.200
Frank -0.800
Dick 1.000
Pairwise correlations in descending order
0.800 Grant and John Not significant
0.800 Orley and Frank Not significant
0.800 Ed and Frank Not significant
0.800 Burt and Frank Not significant
0.600 Ed and Orley Not significant
0.400 Ed and Burt Not significant
0.400 Ed and Grant Not significant
0.400 Grant and Orley Not significant
0.400 Burt and Orley Not significant
0.200 Orley and John Not significant
0.000 Grant and Frank Not significant
-0.200 Ed and John Not significant
-0.200 John and Dick Not significant
-0.400 John and Frank Not significant
-0.400 Burt and Dick Not significant
-0.400 Grant and Dick Not significant
-0.600 Burt and Grant Not significant
-0.600 Ed and Dick Not significant
-0.800 Burt and John Not significant
-0.800 Frank and Dick Not significant
-1.000 Orley and Dick Significantly negative
COMMENT:
This is an astonishing result. Incroyable! Most people were not able to
tell the country of origin of the wines. Think about it: the Long Island
wine comes in first, the Italian wine comes in second, and the Bordeaux
wines come in last. Our best guesses of the current prices are: first
place wine $20, Sassicaia $60, Palmer $60, Cheval Blanc $100. Interest-
ingly, the rainfall in Long Island was about 2/3 of the Bordeaux average,
but much warmer than in Bordeaux. Note that the comparative scores of
the Lenz and Sassicaia on the one hand and the scores of the Cheval
Blanc and Palmer on the other were nearly indistinguishable. However,
from a statistician's point of view, the wines were not significantly
different.
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