WINETASTER ON 12/29/99 WITH 7 JUDGES AND 5 WINES BASED ON RANKS, IDENT=N
Copyright (c) 1995-99 Richard E. Quandt
FLIGHT 1:
Number of Judges = 7
Number of Wines = 5
Identification of the Wine: The judges' overall ranking:
Wine A is J Phelbs,Cabernet,Napa 97 ........ 1st place
Wine B is Sterling Vineyards,Cabernet,Napa 97 ........ 2nd place
Wine C is R Mondavi,Cabernet,Coastal 97 ........ 3rd place
Wine D is Undurraga Reserva,Maipo/Chile 96 ........ 4th place
Wine E is R Mondavi,Cabernet, Napa 96 ........ 5th place
The Judges's Rankings
Judge Wine -> A B C D E
Lisa 1. 2. 5. 3. 4.
Nahomi 2. 1. 4. 3. 5.
Gaby 1. 3. 4. 2. 5.
Keith 2. 1. 4. 3. 5.
Miwa 2. 3. 1. 4. 5.
Alexander 1. 4. 2. 5. 3.
Karl 1. 2. 3. 4. 5.
Table of Votes Against
Wine -> A B C D E
Group Ranking -> 1 2 3 4 5
Votes Against -> 10 16 23 24 32
( 7 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 = 0.5714
The probability that random chance could be responsible for this correlation
is quite small, 0.0030. 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
Karl 0.9747
Nahomi 0.8000
Keith 0.8000
Gaby 0.7000
Lisa 0.7000
Miwa 0.4000
Alexander 0.2000
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 J Phelbs,Cabernet,Napa 97
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2. ........ 2nd place Wine B is Sterling Vineyards,Cabernet,Napa 9
3. ........ 3rd place Wine C is R Mondavi,Cabernet,Coastal 97
4. ........ 4th place Wine D is Undurraga Reserva,Maipo/Chile 96
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5. ........ 5th place Wine E is R Mondavi,Cabernet, Napa 96
We now test whether the ranksums AS A WHOLE provide a significant ordering.
The Friedman Chi-square value is 16.0000. The probability that this could
happen by chance is 0.0030
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
Lisa Nahomi Gaby
Lisa 1.000 0.800 0.800
Nahomi 0.800 1.000 0.700
Gaby 0.800 0.700 1.000
Keith 0.800 1.000 0.700
Miwa 0.000 0.300 0.300
Alexander 0.100 -0.100 0.100
Karl 0.700 0.800 0.700
Keith Miwa Alexander
Lisa 0.800 0.000 0.100
Nahomi 1.000 0.300 -0.100
Gaby 0.700 0.300 0.100
Keith 1.000 0.300 -0.100
Miwa 0.300 1.000 0.600
Alexander -0.100 0.600 1.000
Karl 0.800 0.700 0.500
Karl
Lisa 0.700
Nahomi 0.800
Gaby 0.700
Keith 0.800
Miwa 0.700
Alexander 0.500
Karl 1.000
Pairwise correlations in descending order
1.000 Nahomi and Keith Significantly positive
0.800 Lisa and Gaby Not significant
0.800 Lisa and Nahomi Not significant
0.800 Nahomi and Karl Not significant
0.800 Keith and Karl Not significant
0.800 Lisa and Keith Not significant
0.700 Gaby and Karl Not significant
0.700 Miwa and Karl Not significant
0.700 Nahomi and Gaby Not significant
0.700 Gaby and Keith Not significant
0.700 Lisa and Karl Not significant
0.600 Miwa and Alexander Not significant
0.500 Alexander and Karl Not significant
0.300 Nahomi and Miwa Not significant
0.300 Keith and Miwa Not significant
0.300 Gaby and Miwa Not significant
0.100 Lisa and Alexander Not significant
0.100 Gaby and Alexander Not significant
0.000 Lisa and Miwa Not significant
-0.100 Nahomi and Alexander Not significant
-0.100 Keith and Alexander Not significant
COMMENT:
Most of the judges were not expierenced in drinking wine let alone in
doing wine tastings. Nevertheless everyone agrees that the Joseph
Phelbs is an outstanding wine. The included supermarket-wine from
Chile was considered to be the worst. The Mondavi Napa Cabernet was corked
and should have been excluded from the tasting.
Interesting is also a simple regression between ranking and price for
the correlation seems to be almost perfect. The retailer prices were:
Joseph Phelbs: $31.39
Sterling Vineyards: $19.99
Mondavi Coastal: $ 8.99
Undurraga Reserva: $ 7.99
Mondavi Napa Valley:$23.29