WINETASTER ON 04/20/01 WITH 4 JUDGES AND 3 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2000 Richard E. Quandt
FLIGHT 1: Number of Judges = 4 Number of Wines = 3
Identification of the Wine: The judges' overall ranking:
Wine A is Bonnes-Mares 1985, Mugnier ........ 1st place Wine B is Clos St. Denis 1985, Castagnier ........ 3rd place Wine C is Gevrey Chambertin 1985, St.Jacques ........ 2nd place
The Judges's Rankings
Judge Wine -> A B C Orley 1. 2. 3. Gina 1. 3. 2. Highgate 2. 3. 1. Dick 1. 2. 3.
Table of Votes Against Wine -> A B C
Group Ranking -> 1 3 2 Votes Against -> 5 10 9
( 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 = 0.4375
The probability that random chance could be responsible for this correlation is rather large, 0.1738. 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 Gina 0.8660 Orley 0.5000 Dick 0.5000 Highgate -0.5000
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 Bonnes-Mares 1985, Mugnier 2. ........ 2nd place Wine C is Gevrey Chambertin 1985, St.Jacques 3. ........ 3rd place Wine B is Clos St. Denis 1985, Castagnier We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 3.5000. The probability that this could happen by chance is 0.1738 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 Orley Gina Highgate Orley 1.000 0.500 -0.500 Gina 0.500 1.000 0.500 Highgate -0.500 0.500 1.000 Dick 1.000 0.500 -0.500 Dick Orley 1.000 Gina 0.500 Highgate -0.500 Dick 1.000 Pairwise correlations in descending order 1.000 Orley and Dick Significantly positive 0.500 Orley and Gina Not significant 0.500 Gina and Dick Not significant 0.500 Gina and Highgate Not significant -0.500 Orley and Highgate Not significant -0.500 Highgate and Dick Not significant
COMMENT: Every wine was absolutely superb. There was no stinker in this group of 1985 Burgundies. These seemed like really authentic examples of the vineyards they were expected to represent. As the only former Wines Officer of the Fourth Royal Horse Artillery present, and as the only one present never to have participated in a wine tasting, Highgate feels that his views should be accorded a weight less than one; however, he can record with probability 1.0 that wines like these were never served in the Fourth Royal Artillery. The reason why Gina likes the Gevrey- Chambertin is becuse it is really ready to drink. The reason why Dick liked the Bonnes-Mares best is because it is the spiciest of the wines.
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