WINETASTER ON 02/15/99 WITH 7 JUDGES AND 4 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-98 Richard E. Quandt

FLIGHT 1: Number of Judges = 7 Number of Wines = 4
Identification of the Wine: The judges' overall ranking:
Wine A is Lenz 1988 ........ 1st place Wine B is Sassicaia 1988 ........ 2nd place Wine C is Ch. Palmer 1988 ........ 4th place Wine D is Ch. Cheval Blanc 1988 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D Ed 1. 2. 3. 4. Burt 3. 1. 2. 4. Grant 1. 3. 4. 2. Orley 2. 1. 4. 3. John 2. 3. 4. 1. Frank 2. 1. 3. 4. Dick 3. 4. 1. 2.
Table of Votes Against Wine -> A B C D
Group Ranking -> 1 2 4 3 Votes Against -> 14 15 21 20
( 7 is the best possible, 28 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 = 0.1510

The probability that random chance could be responsible for this correlation is rather large, 0.3659. 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 0.7379 Orley 0.7379 Frank 0.6000 Burt 0.0000 Grant 0.0000 John -0.3162 Dick -0.9487

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 A is Lenz 1988 2. ........ 2nd place Wine B is Sassicaia 1988 3. ........ 3rd place Wine D is Ch. Cheval Blanc 1988 4. ........ 4th place Wine C is Ch. Palmer 1988 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 3.1714. The probability that this could happen by chance is 0.3659 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 1.00 for significance at the 0.05 level and must exceed 1.00 for significance at the 0.1 level Ed Burt Grant Ed 1.000 0.400 0.400 Burt 0.400 1.000 -0.600 Grant 0.400 -0.600 1.000 Orley 0.600 0.400 0.400 John -0.200 -0.800 0.800 Frank 0.800 0.800 0.000 Dick -0.600 -0.400 -0.400 Orley John Frank Ed 0.600 -0.200 0.800 Burt 0.400 -0.800 0.800 Grant 0.400 0.800 0.000 Orley 1.000 0.200 0.800 John 0.200 1.000 -0.400 Frank 0.800 -0.400 1.000 Dick -1.000 -0.200 -0.800 Dick Ed -0.600 Burt -0.400 Grant -0.400 Orley -1.000 John -0.200 Frank -0.800 Dick 1.000 Pairwise correlations in descending order 0.800 Grant and John Not significant 0.800 Orley and Frank Not significant 0.800 Ed and Frank Not significant 0.800 Burt and Frank Not significant 0.600 Ed and Orley Not significant 0.400 Ed and Burt Not significant 0.400 Ed and Grant Not significant 0.400 Grant and Orley Not significant 0.400 Burt and Orley Not significant 0.200 Orley and John Not significant 0.000 Grant and Frank Not significant -0.200 Ed and John Not significant -0.200 John and Dick Not significant -0.400 John and Frank Not significant -0.400 Burt and Dick Not significant -0.400 Grant and Dick Not significant -0.600 Burt and Grant Not significant -0.600 Ed and Dick Not significant -0.800 Burt and John Not significant -0.800 Frank and Dick Not significant -1.000 Orley and Dick Significantly negative

COMMENT: This is an astonishing result. Incroyable! Most people were not able to tell the country of origin of the wines. Think about it: the Long Island wine comes in first, the Italian wine comes in second, and the Bordeaux wines come in last. Our best guesses of the current prices are: first place wine $20, Sassicaia $60, Palmer $60, Cheval Blanc $100. Interest- ingly, the rainfall in Long Island was about 2/3 of the Bordeaux average, but much warmer than in Bordeaux. Note that the comparative scores of the Lenz and Sassicaia on the one hand and the scores of the Cheval Blanc and Palmer on the other were nearly indistinguishable. However, from a statistician's point of view, the wines were not significantly different.
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