WINETASTER ON 02/02/15 WITH 8 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2015 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 Stags Leap, SLV, 2003 ........ 2nd place Wine B is Chimney Rock, Elevage, 2004 ........ 4th place Wine C is Dunn, Howell, 1999 tied for 7th place Wine D is Whitehall Lane 1997 ........ 6th place Wine E is Grgich Hills, 1999 ........ 1st place Wine F is Etude, 2002 ........ 5th place Wine G is Dominus 1999 tied for 7th place Wine H is Chimney Rock, Alpine, 2004 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D E F G H Mike 3. 1. 7. 4. 5. 8. 6. 2. Frank 4. 5. 8. 1. 7. 3. 6. 2. Orley 3. 4. 2. 8. 1. 5. 6. 7. Zaki 5. 7. 8. 4. 6. 2. 3. 1. Burt 2. 5. 6. 8. 3. 7. 4. 1. Ed 2. 4. 5. 8. 1. 3. 7. 6. Bob 2. 3. 8. 6. 1. 4. 7. 5. Dick 6. 4. 3. 5. 1. 2. 8. 7.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 2 4 7 6 1 5 7 3 Votes Against -> 27 33 47 44 25 34 47 31
( 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 = 0.2031
The probability that random chance could be responsible for this correlation is rather large, 0.1231. 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 Bob 0.8982 Ed 0.6467 Burt 0.3095 Orley 0.1596 Mike 0.1317 Dick -0.0361 Frank -0.2619 Zaki -0.2619
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 Grgich Hills, 1999 2. ........ 2nd place Wine A is Stags Leap, SLV, 2003 3. ........ 3rd place Wine H is Chimney Rock, Alpine, 2004 4. ........ 4th place Wine B is Chimney Rock, Elevage, 2004 5. ........ 5th place Wine F is Etude, 2002 6. ........ 6th place Wine D is Whitehall Lane 1997 --------------------------------------------------- 7. tied for 7th place Wine C is Dunn, Howell, 1999 8. tied for 7th place Wine G is Dominus 1999 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 11.3750. The probability that this could happen by chance is 0.1231 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 Mike Frank Orley Mike 1.000 0.333 -0.190 Frank 0.333 1.000 -0.810 Orley -0.190 -0.810 1.000 Zaki -0.048 0.690 -0.714 Burt 0.476 -0.119 0.214 Ed -0.048 -0.381 0.810 Bob 0.381 0.048 0.429 Dick -0.381 -0.333 0.619 Zaki Burt Ed Mike -0.048 0.476 -0.048 Frank 0.690 -0.119 -0.381 Orley -0.714 0.214 0.810 Zaki 1.000 0.190 -0.310 Burt 0.190 1.000 0.333 Ed -0.310 0.333 1.000 Bob -0.071 0.405 0.810 Dick -0.452 -0.381 0.619 Bob Dick Mike 0.381 -0.381 Frank 0.048 -0.333 Orley 0.429 0.619 Zaki -0.071 -0.452 Burt 0.405 -0.381 Ed 0.810 0.619 Bob 1.000 0.381 Dick 0.381 1.000 Pairwise correlations in descending order 0.810 Orley and Ed Significantly positive 0.810 Ed and Bob Significantly positive 0.690 Frank and Zaki Significantly positive 0.619 Orley and Dick Not significant 0.619 Ed and Dick Not significant 0.476 Mike and Burt Not significant 0.429 Orley and Bob Not significant 0.405 Burt and Bob Not significant 0.381 Bob and Dick Not significant 0.381 Mike and Bob Not significant 0.333 Mike and Frank Not significant 0.333 Burt and Ed Not significant 0.214 Orley and Burt Not significant 0.190 Zaki and Burt Not significant 0.048 Frank and Bob Not significant -0.048 Mike and Zaki Not significant -0.048 Mike and Ed Not significant -0.071 Zaki and Bob Not significant -0.119 Frank and Burt Not significant -0.190 Mike and Orley Not significant -0.310 Zaki and Ed Not significant -0.333 Frank and Dick Not significant -0.381 Frank and Ed Not significant -0.381 Burt and Dick Not significant -0.381 Mike and Dick Not significant -0.452 Zaki and Dick Not significant -0.714 Orley and Zaki Significantly negative -0.810 Frank and Orley Significantly negative
COMMENT: These were excellent wines. Two tasters thought that wine D, the Whitehall Lane cabernet, was slightly oxidized. Wine E, the Grgich Hills, was preferred by many tasters but it is not normally considered in the top rank of cabernets. What a pleasant surprise. One of us remarked and the orthers agreed that there seemed to be little correlation between preferences and vintages. We all agreed these were typical Napa wines, not monstrous fruit bombs. Relative to other tasting, the group felt that these wines were difficult to distinguish. Some might think that it is puzzling that the Grgich Hills did not merit being significantly good according to the statistical test, in spite of the facts that it scored the smallest "votes" against and that it was scored best by four tasters. However, the runner-up was very close in terms of votes against and wines B and H were also close behind, which, so-to-speak, statistically diluted the effect on wine E.
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