WINETASTER ON 12/18/98 WITH 9 JUDGES AND 9 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-98 Richard E. Quandt
FLIGHT 1: Number of Judges = 9 Number of Wines = 9
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. de Marsannay 93 ........ 5th place Wine B is WG Thuengersheimer Johannisberg Kabinet 94 ........ 9th place Wine C is Knipser,Laumersch Kirschgarten Spaetlese 94 ........ 6th place Wine D is Perrot-Minot Chambolle Musigny 1er Cru 94 ........ 4th place Wine E is Chevillon, Nuit-St.Georges 94 ........ 7th place Wine F is Lavirotte,Santenay Clos des Mouches 94 ........ 8th place Wine G is Michelot,Nuit-St.Georges Les Poret 94 ........ 3rd place Wine H is Bichot,Les Echezeaux Grand Cru 94 ........ 1st place Wine I is Coli, Corton-Renardes Gran Cru 93 ........ 2nd place
The Judges's Rankings
Judge Wine -> A B C D E F G H I Andre 5. 9. 2. 6. 8. 7. 4. 3. 1. Amo 4. 8. 7. 6. 5. 9. 2. 1. 3. Heike 1. 9. 4. 5. 6. 7. 8. 3. 2. Kai 3. 9. 8. 2. 5. 4. 6. 1. 7. Karl 7. 9. 3. 4. 8. 6. 5. 2. 1. Michael 6. 8. 7. 3. 5. 9. 2. 1. 4. Pit 6. 7. 5. 2. 4. 3. 1. 9. 8. Roland 6. 9. 4. 5. 8. 7. 2. 3. 1. Wolfgang 3. 8. 5. 2. 9. 7. 4. 1. 6.
Table of Votes Against Wine -> A B C D E F G H I
Group Ranking -> 5 9 6 4 7 8 3 1 2 Votes Against -> 41 76 45 35 58 59 34 24 33
( 9 is the best possible, 81 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 = 0.4420
The probability that random chance could be responsible for this correlation is quite small, 0.0001. 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 Michael 0.8117 Roland 0.7615 Wolfgang 0.7333 Amo 0.7000 Karl 0.6833 Andre 0.6000 Heike 0.4100 Kai 0.3667 Pit -0.2427
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 H is Bichot,Les Echezeaux Grand Cru 94 --------------------------------------------------- 2. ........ 2nd place Wine I is Coli, Corton-Renardes Gran Cru 93 3. ........ 3rd place Wine G is Michelot,Nuit-St.Georges Les Poret 94 4. ........ 4th place Wine D is Perrot-Minot Chambolle Musigny 1er 94 5. ........ 5th place Wine A is Ch. de Marsannay 93 6. ........ 6th place Wine C is Knipser,Laumersch Kirschgarten Spaetlese 94 7. ........ 7th place Wine E is Chevillon, Nuit-St.Georges 94 --------------------------------------------------- 8. ........ 8th place Wine F is Lavirotte,Santenay Clos des Mouches 94 9. ........ 9th place Wine B is WG Thuengersheimer Johannisberg Kabinet 94 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 31.8222. The probability that this could happen by chance is 0.0001 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 0.70 for significance at the 0.05 level and must exceed 0.60 for significance at the 0.1 level Andre Amo Heike Andre 1.000 0.567 0.650 Amo 0.567 1.000 0.450 Heike 0.650 0.450 1.000 Kai 0.017 0.367 0.400 Karl 0.900 0.483 0.550 Michael 0.450 0.883 0.267 Pit -0.300 -0.267 -0.500 Roland 0.917 0.700 0.450 Wolfgang 0.500 0.550 0.500 Kai Karl Michael Andre 0.017 0.900 0.450 Amo 0.367 0.483 0.883 Heike 0.400 0.550 0.267 Kai 1.000 0.200 0.483 Karl 0.200 1.000 0.533 Michael 0.483 0.533 1.000 Pit 0.050 -0.267 -0.033 Roland 0.100 0.883 0.667 Wolfgang 0.667 0.550 0.650 Pit Roland Wolfgang Andre -0.300 0.917 0.500 Amo -0.267 0.700 0.550 Heike -0.500 0.450 0.500 Kai 0.050 0.100 0.667 Karl -0.267 0.883 0.550 Michael -0.033 0.667 0.650 Pit 1.000 -0.100 -0.067 Roland -0.100 1.000 0.550 Wolfgang -0.067 0.550 1.000 Pairwise correlations in descending order 0.917 Andre and Roland Significantly positive 0.900 Andre and Karl Significantly positive 0.883 Amo and Michael Significantly positive 0.883 Karl and Roland Significantly positive 0.700 Amo and Roland Significantly positive 0.667 Michael and Roland Significantly positive 0.667 Kai and Wolfgang Significantly positive 0.650 Andre and Heike Significantly positive 0.650 Michael and Wolfgang Significantly positive 0.567 Andre and Amo Not significant 0.550 Roland and Wolfgang Not significant 0.550 Karl and Wolfgang Not significant 0.550 Heike and Karl Not significant 0.550 Amo and Wolfgang Not significant 0.533 Karl and Michael Not significant 0.500 Andre and Wolfgang Not significant 0.500 Heike and Wolfgang Not significant 0.483 Amo and Karl Not significant 0.483 Kai and Michael Not significant 0.450 Andre and Michael Not significant 0.450 Heike and Roland Not significant 0.450 Amo and Heike Not significant 0.400 Heike and Kai Not significant 0.367 Amo and Kai Not significant 0.267 Heike and Michael Not significant 0.200 Kai and Karl Not significant 0.100 Kai and Roland Not significant 0.050 Kai and Pit Not significant 0.017 Andre and Kai Not significant -0.033 Michael and Pit Not significant -0.067 Pit and Wolfgang Not significant -0.100 Pit and Roland Not significant -0.267 Karl and Pit Not significant -0.267 Amo and Pit Not significant -0.300 Andre and Pit Not significant -0.500 Heike and Pit Not significant
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