WINETASTER ON 09/20/99 WITH 6 JUDGES AND 5 WINES BASED ON RANKS, IDENT=N
Copyright (c) 1995-99 Richard E. Quandt
FLIGHT 1:
Number of Judges = 6
Number of Wines = 5
Identification of the Wine: The judges' overall ranking:
Wine A is Chambertin Bouree '85 ........ 1st place
Wine B is Volnay Champan Angerville '85 ........ 2nd place
Wine C is Nuits St. Georges Chaillots R. Dubois '85 ........ 4th place
Wine D is Nuits St. Georges Vaucrain H. Gouge '85 ........ 3rd place
Wine E is Gevrey Chambertin R Groffier '85 ........ 5th place
The Judges's Rankings
Judge Wine -> A B C D E
Grant 1. 2. 4. 3. 5.
Frank 4. 1. 2. 3. 5.
Orley 1. 5. 4. 3. 2.
John 2. 1. 3. 5. 4.
Burt 1. 3. 5. 2. 4.
Dick 3. 2. 4. 1. 5.
Table of Votes Against
Wine -> A B C D E
Group Ranking -> 1 2 4 3 5
Votes Against -> 12 14 22 17 25
( 6 is the best possible, 30 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 = 0.3278
The probability that random chance could be responsible for this correlation
is quite small, 0.0966. 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 1.0000
Burt 0.7182
Dick 0.6000
John 0.2000
Frank 0.1539
Orley -0.3000
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 Chambertin Bouree '85
2. ........ 2nd place Wine B is Volnay Champan Angerville '85
3. ........ 3rd place Wine D is Nuits St. Georges Vaucrain H. Goug
4. ........ 4th place Wine C is Nuits St. Georges Chaillots R. Dub
---------------------------------------------------
5. ........ 5th place Wine E is Gevrey Chambertin R Groffier '85
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 7.8667. The probability that this could
happen by chance is 0.0966
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 0.90 for significance at the 0.1 level
Grant Frank Orley
Grant 1.000 0.300 0.100
Frank 0.300 1.000 -0.900
Orley 0.100 -0.900 1.000
John 0.600 0.500 -0.300
Burt 0.800 -0.200 0.500
Dick 0.600 0.500 -0.300
John Burt Dick
Grant 0.600 0.800 0.600
Frank 0.500 -0.200 0.500
Orley -0.300 0.500 -0.300
John 1.000 0.100 0.000
Burt 0.100 1.000 0.600
Dick 0.000 0.600 1.000
Pairwise correlations in descending order
0.800 Grant and Burt Not significant
0.600 Grant and Dick Not significant
0.600 Grant and John Not significant
0.600 Burt and Dick Not significant
0.500 Frank and Dick Not significant
0.500 Frank and John Not significant
0.500 Orley and Burt Not significant
0.300 Grant and Frank Not significant
0.100 John and Burt Not significant
0.100 Grant and Orley Not significant
0.000 John and Dick Not significant
-0.200 Frank and Burt Not significant
-0.300 Orley and John Not significant
-0.300 Orley and Dick Not significant
-0.900 Frank and Orley Significantly negative
COMMENT:
Everybody liked all the wines; it was a wonderful tasting. Burt says
that the Chambertin Bouree was smooth and absolutely delicious. Dick says
that the Gervey Chambertin had a particularly tobacco-ish taste.
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