WINETASTER ON 3/6/95 WITH 5 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2011 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 5 Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is Barbaresco Sori San Lorenzo 1990 ........ 4th place Wine B is Barbaresco Sori San Lorenzo 1978 tied for 1st place Wine C is Barolo Sperss 1988 tied for 1st place Wine D is Barbaresco Sori Tilden 1990 tied for 6th place Wine E is Barbaresco Sori Tilden 1978 ........ 3rd place Wine F is Barolo Sperss 1989 ........ 5th place Wine G is Barbaresco Sori San Lorenzo 1989 tied for 6th place
The Judges's Rankings
Judge Wine -> A B C D E F G Dick 4. 3. 2. 7. 1. 6. 5. Orley 4. 3. 1. 5. 6. 2. 7. John 3. 4. 5. 7. 1. 6. 2. Bob 1. 2. 5. 3. 4. 6. 7. Burt 7. 3. 2. 5. 4. 1. 6.
Table of Votes Against Wine -> A B C D E F G
Group Ranking -> 4 1 1 6 3 5 6 Votes Against -> 19 15 15 27 16 21 27
( 5 is the best possible, 35 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 = 0.2371
The probability that random chance could be responsible for this correlation is rather large, 0.3104. 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 Dick 0.5930 Orley 0.2143 Burt 0.0000 Bob -0.0357 John -0.1261
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 B is Barbaresco Sori San Lorenzo 1978 2. tied for 1st place Wine C is Barolo Sperss 1988 3. ........ 3rd place Wine E is Barbaresco Sori Tilden 1978 4. ........ 4th place Wine A is Barbaresco Sori San Lorenzo 1990 5. ........ 5th place Wine F is Barolo Sperss 1989 --------------------------------------------------- 6. tied for 6th place Wine D is Barbaresco Sori Tilden 1990 7. tied for 6th place Wine G is Barbaresco Sori San Lorenzo 1989 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 7.1143. The probability that this could happen by chance is 0.3104 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 Orley John Dick 1.000 0.107 0.643 Orley 0.107 1.000 -0.571 John 0.643 -0.571 1.000 Bob 0.143 0.107 -0.036 Burt 0.143 0.714 -0.429 Bob Burt Dick 0.143 0.143 Orley 0.107 0.714 John -0.036 -0.429 Bob 1.000 -0.357 Burt -0.357 1.000 Pairwise correlations in descending order 0.714 Orley and Burt Significantly positive 0.643 Dick and John Not significant 0.143 Dick and Bob Not significant 0.143 Dick and Burt Not significant 0.107 Dick and Orley Not significant 0.107 Orley and Bob Not significant -0.036 John and Bob Not significant -0.357 Bob and Burt Not significant -0.429 John and Burt Not significant -0.571 Orley and John Not significant
COMMENT: While the agreement in the group was not strong, it seems fairly clear that the 1978 ans 1988 were preferred to the 1989 and 1990.
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