WINETASTER ON 03/10/22 WITH 8 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2022 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 8 Number of Wines = 8
Identification of the Wine: The judges' overall ranking:
Wine A is Gedvrey-Chambertin 1er Cru 1997 ........ 6th place Wine B is Vosne-Romanee 1er Cru 2001 ........ 7th place Wine C is Chapelle-Chambertin GC 1996 ........ 8th place Wine D is Corton-Bressandes GC 2008 ........ 2nd place Wine E is Corton Latour GC 2007 ........ 5th place Wine F is Latricieres Chambertin GC 1999 ........ 4th place Wine G is Volnay Santenots 1er Cru 1999 ........ 1st place Wine H is Beaune Bressandes 1er Cru 2005 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D E F G H David 6. 1. 7. 2. 8. 5. 4. 3. Zaki 7. 8. 6. 4. 5. 1. 2. 3. Mike 8. 4. 7. 3. 2. 5. 1. 6. Ed 6. 8. 7. 5. 3. 2. 1. 4. Frank 6. 5. 1. 2. 3. 8. 4. 7. Angus 2. 8. 3. 7. 5. 4. 1. 6. Bob 1. 5. 8. 6. 7. 3. 2. 4. Dick 5. 6. 8. 4. 3. 7. 2. 1.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 6 7 8 2 5 4 1 3 Votes Against -> 41 45 47 33 36 35 17 34
( 8 is the best possible, 64 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 = 0.2240
The probability that random chance could be responsible for this correlation is quite small, 0.0841. 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 0.7545 Zaki 0.5784 Dick 0.4579 Mike 0.2874 Angus -0.0599 Bob -0.0719 David -0.2755 Frank -0.4431
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 G is Volnay Santenots 1er Cru 1999 --------------------------------------------------- 2. ........ 2nd place Wine D is Corton-Bressandes GC 2008 3. ........ 3rd place Wine H is Beaune Bressandes 1er Cru 2005 4. ........ 4th place Wine F is Latricieres Chambertin GC 1999 5. ........ 5th place Wine E is Corton Latour GC 2007 6. ........ 6th place Wine A is Gedvrey-Chambertin 1er Cru 1997 7. ........ 7th place Wine B is Vosne-Romanee 1er Cru 2001 --------------------------------------------------- 8. ........ 8th place Wine C is Chapelle-Chambertin GC 1006 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 12.5417. The probability that this could happen by chance is 0.0841 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 David Zaki Mike David 1.000 0.000 0.190 Zaki 0.000 1.000 0.357 Mike 0.190 0.357 1.000 Ed -0.214 0.881 0.548 Frank -0.214 -0.333 0.262 Angus -0.595 0.262 -0.119 Bob 0.190 0.262 -0.119 Dick 0.190 0.333 0.452 Ed Frank Angus David -0.214 -0.214 -0.595 Zaki 0.881 -0.333 0.262 Mike 0.548 0.262 -0.119 Ed 1.000 -0.286 0.429 Frank -0.286 1.000 0.000 Angus 0.429 0.000 1.000 Bob 0.357 -0.714 0.452 Dick 0.500 -0.143 -0.024 Bob Dick David 0.190 0.190 Zaki 0.262 0.333 Mike -0.119 0.452 Ed 0.357 0.500 Frank -0.714 -0.143 Angus 0.452 -0.024 Bob 1.000 0.262 Dick 0.262 1.000 Pairwise correlations in descending order 0.881 Zaki and Ed Significantly positive 0.548 Mike and Ed Not significant 0.500 Ed and Dick Not significant 0.452 Angus and Bob Not significant 0.452 Mike and Dick Not significant 0.429 Ed and Angus Not significant 0.357 Zaki and Mike Not significant 0.357 Ed and Bob Not significant 0.333 Zaki and Dick Not significant 0.262 Zaki and Bob Not significant 0.262 Mike and Frank Not significant 0.262 Bob and Dick Not significant 0.262 Zaki and Angus Not significant 0.190 David and Dick Not significant 0.190 David and Mike Not significant 0.190 David and Bob Not significant 0.000 Frank and Angus Not significant 0.000 David and Zaki Not significant -0.024 Angus and Dick Not significant -0.119 Mike and Angus Not significant -0.119 Mike and Bob Not significant -0.143 Frank and Dick Not significant -0.214 David and Ed Not significant -0.214 David and Frank Not significant -0.286 Ed and Frank Not significant -0.333 Zaki and Frank Not significant -0.595 David and Angus Not significant -0.714 Frank and Bob Significantly negative
COMMENT: The wiones were all delicious, with relatively small differences among them. Four of the eight wines were grand cru and the emaining eight premier cru. An obvcious test is to see if there is a significant difference between these two groups. The answer is in the negative; while the ranksum for the grand cru wines is slightly smalller than for the premier cru wines, the differendce is not significant. A similar test can be performed between the group of four relatively young wines and the group of relatively older ones, and again no significant difference is found.
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