WINETASTER ON 03/06/00 WITH 5 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2000 Richard E. Quandt FLIGHT 1: Number of Judges = 5 Number of Wines = 8 Identification of the Wine: The judges' overall ranking: Wine A is Chablis 1Cru "Vaucopin"97 JP Grossot ........ 7th place Wine B is Pouilly Fusse "Ronchevats"97 Saumaize-Michelin ....... 2nd place Wine C is Chablis AC Domaine Manants 97,Brocard ........ 8th place Wine D is Chablis 1Cru "Fourneaux"97,JP Grosot ........ 5th place Wine E is Chablis AC "Champs Royau"97, Maladiere ........ 1st place Wine F is Chablis 1Cru "Montmains"97,Maladiere ........ 3rd place Wine G is Chablis AC 97, JP Grossot ........ 6th place Wine H is Chablis 1Cru "Montmains"97, Brocard ........ 4th place The Judges's Rankings Judge Wine -> A B C D E F G H Manfred 7. 3. 8. 5. 1. 2. 4. 6. Wolfgang 5. 2. 8. 3. 1. 4. 6. 7. Andre 8. 1. 7. 6. 3. 4. 5. 2. Bernd 2. 3. 7. 5. 4. 6. 8. 1. Kai 6. 3. 8. 5. 1. 4. 2. 7. Table of Votes Against Wine -> A B C D E F G H Group Ranking -> 7 2 8 5 1 3 6 4 Votes Against -> 28 12 38 24 10 20 25 23 ( 5 is the best possible, 40 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 = 0.5257 The probability that random chance could be responsible for this correlation is quite small, 0.0103. 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 Manfred 0.7350 Wolfgang 0.6826 Kai 0.5181 Andre 0.4910 Bernd -0.0238 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 E is Chablis AC"Champs Royau"97, Maladi 2. ........ 2nd place Wine B is Pouilly Fusse "Ronchevats"97 Sauma --------------------------------------------------- 3. ........ 3rd place Wine F is Chablis 1Cru "Montmains"97,Maladie 4. ........ 4th place Wine H is Chablis 1Cru "Montmains"97, Brocar 5. ........ 5th place Wine D is Chablis 1Cru "Fourneaux"97,JP Gros 6. ........ 6th place Wine G is Chablis AC 97, JP Grossot 7. ........ 7th place Wine A is Chablis 1Cru "Vaucopin"97 JP Gross --------------------------------------------------- 8. ........ 8th place Wine C is Chablis AC Domaine Manants 97,Broc We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 18.4000. The probability that this could happen by chance is 0.0103 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 0.74 for significance at the 0.05 level and must exceed 0.64 for significance at the 0.1 level Manfred Wolfgang Andre Manfred 1.000 0.786 0.619 Wolfgang 0.786 1.000 0.405 Andre 0.619 0.405 1.000 Bernd -0.095 0.190 0.333 Kai 0.881 0.738 0.429 Bernd Kai Manfred -0.095 0.881 Wolfgang 0.190 0.738 Andre 0.333 0.429 Bernd 1.000 -0.214 Kai -0.214 1.000 Pairwise correlations in descending order 0.881 Manfred and Kai Significantly positive 0.786 Manfred and Wolfgang Significantly positive 0.738 Wolfgang and Kai Significantly positive 0.619 Manfred and Andre Not significant 0.429 Andre and Kai Not significant 0.405 Wolfgang and Andre Not significant 0.333 Andre and Bernd Not significant 0.190 Wolfgang and Bernd Not significant -0.095 Manfred and Bernd Not significant -0.214 Bernd and Kai Not significant
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