WINETASTER ON 2/14/94 WITH 7 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2011 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 7 Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is Sassicaia 1981 ........ 7th place Wine B is Sassicaia 1978 ........ 6th place Wine C is Sassicaia 1988 ........ 1st place Wine D is Sassicaia 1985 ........ 5th place Wine E is Sassicaia 1990 tied for 3rd place Wine F is Sassicaia 1986 ........ 2nd place Wine G is Sassicaia 1982 tied for 3rd place
The Judges's Rankings
Judge Wine -> A B C D E F G Dick 7. 6. 3. 4. 5. 1. 2. Ed 6. 4. 3. 2. 1. 5. 7. Frank 7. 4. 6. 5. 3. 2. 1. Bob 4. 7. 1. 2. 5. 6. 3. Orley 7. 6. 1. 2. 5. 4. 3. Burt 7. 6. 1. 5. 3. 4. 2. John 4. 5. 3. 7. 2. 1. 6.
Table of Votes Against Wine -> A B C D E F G
Group Ranking -> 7 6 1 5 3 2 3 Votes Against -> 42 38 18 27 24 23 24
( 7 is the best possible, 49 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 = 0.3309
The probability that random chance could be responsible for this correlation is quite small, 0.0308. 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 Burt 0.8108 Orley 0.6667 Dick 0.5946 Bob 0.1982 Frank 0.1622 Ed 0.0000 John -0.1622
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 C is Sassicaia 1988 --------------------------------------------------- 2. ........ 2nd place Wine F is Sassicaia 1986 3. tied for 3rd place Wine G is Sassicaia 1982 4. tied for 3rd place Wine E is Sassicaia 1990 5. ........ 5th place Wine D is Sassicaia 1985 --------------------------------------------------- 6. ........ 6th place Wine B is Sassicaia 1978 7. ........ 7th place Wine A is Sassicaia 1981 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 13.8980. The probability that this could happen by chance is 0.0308 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 0.79 for significance at the 0.05 level and must exceed 0.71 for significance at the 0.1 level Dick Ed Frank Dick 1.000 -0.179 0.643 Ed -0.179 1.000 -0.214 Frank 0.643 -0.214 1.000 Bob 0.214 0.107 -0.357 Orley 0.679 0.250 0.107 Burt 0.679 0.143 0.393 John 0.214 0.143 0.107 Bob Orley Burt Dick 0.214 0.679 0.679 Ed 0.107 0.250 0.143 Frank -0.357 0.107 0.393 Bob 1.000 0.750 0.500 Orley 0.750 1.000 0.750 Burt 0.500 0.750 1.000 John -0.357 -0.179 0.214 John Dick 0.214 Ed 0.143 Frank 0.107 Bob -0.357 Orley -0.179 Burt 0.214 John 1.000 Pairwise correlations in descending order 0.750 Bob and Orley Significantly positive 0.750 Orley and Burt Significantly positive 0.679 Dick and Burt Not significant 0.679 Dick and Orley Not significant 0.643 Dick and Frank Not significant 0.500 Bob and Burt Not significant 0.393 Frank and Burt Not significant 0.250 Ed and Orley Not significant 0.214 Burt and John Not significant 0.214 Dick and Bob Not significant 0.214 Dick and John Not significant 0.143 Ed and Burt Not significant 0.143 Ed and John Not significant 0.107 Ed and Bob Not significant 0.107 Frank and Orley Not significant 0.107 Frank and John Not significant -0.179 Orley and John Not significant -0.179 Dick and Ed Not significant -0.214 Ed and Frank Not significant -0.357 Bob and John Not significant -0.357 Frank and Bob Not significant
COMMENT: All of these wines are Sassicaia Te nuta San Guido, and it is to be noted that there was remarkable agreement among the judges.
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