WINETASTER ON 01/02/06 WITH 4 JUDGES AND 3 WINES BASED ON RANKS, IDENT=Y Copyright (c) 1995-2006 Richard E. Quandt, V. 1.65
A Tasting of Tokaji Aszú Wines from the Royal Tokaji Company
FLIGHT 1: Number of Judges = 4 Number of Wines = 3
Identification of the Wine: The judges' overall ranking:
Wine A is Tokaji Aszu 6 putt. 1993 tied for 1st place Wine B is Tokaji Aszu Essencia 1993 ........ 3rd place Wine C is Tokaji Aszu 5 putt. 1993 tied for 1st place
The Judges's Rankings
Judge Wine -> A B C Frank 1. 3. 2. Amanda 2. 3. 1. John 2. 3. 1. Dick 2. 1. 3.
Table of Votes Against Wine -> A B C
Group Ranking -> 1 3 1 Votes Against -> 7 10 7
( 4 is the best possible, 12 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 = 0.1875
The probability that random chance could be responsible for this correlation is rather large, 0.4724. 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.
The correlation I measures the degree to which the identification of each judge is correlated with the truth. Here a 1.0 means that the judge identified the wines perfectly, and a 0 means that he identified none of them.
Correlation Between the Ranks of Each Person With the Average Ranking of Others
Name of Person Correlation R Frank 0.5000 Amanda 0.5000 John 0.5000 Dick -1.0000
Next, we show the correlation among the wine identifications of the judges, which also ranges between 1.0 and 0.0:
C = 0.2500
The probability that random chance could be responsible for this correlation is quite small: < 5 %. Most people would say that unless this probability is less than 0.1, the judges' identifications are not highly related.
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. tied for 1st place Wine A is Tokaji Aszu 6 putt. 1993 2. tied for 1st place Wine C is Tokaji Aszu 5 putt. 1993 3. ........ 3rd place Wine B is Tokaji Aszu Essencia 1993 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 1.5000. The probability that this could happen by chance is 0.4724 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 Frank Amanda John Frank 1.000 0.500 0.500 Amanda 0.500 1.000 1.000 John 0.500 1.000 1.000 Dick -0.500 -1.000 -1.000 Dick Frank -0.500 Amanda -1.000 John -1.000 Dick 1.000 Pairwise correlations in descending order 1.000 Amanda and John Significantly positive 0.500 Frank and John Not significant 0.500 Frank and Amanda Not significant -0.500 Frank and Dick Not significant -1.000 Amanda and Dick Significantly negative -1.000 John and Dick Significantly negative
COMMENT: All three wines had a dark amber color, with wine C perhaps a shade lighter. One taster thought that the Essencia needed some more glass time. This taster almost changed his mind at the time that the votes were cast. Another taster thought that wine C (5 puttonyos) had a bitter aftertaste and that B (the essencia) was the smoothest with a lovely oily texture. The three judges who ranked the essencia last, struggled mightily to tell the difference between A and C. We also tasted a late harvest St. Jean, 1982, riesling (not included in the rankings)and it acquitted itself very well against this competition.
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