WINETASTER ON 12/07/20 WITH 5 JUDGES AND 6 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2020 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 5 Number of Wines = 6
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Cheval Blanc 1997 tied for 4th place Wine B is Ch. Latour 1997 ........ 3rd place Wine C is Ch. Palmer 1997 ........ 1st place Wine D is Ch, Margaux 1998 ........ 2nd place Wine E is Ch. Latour 1998 tied for 4th place Wine F is Ch. Haut Brion 1997 ........ 6th place
The Judges's Rankings
Judge Wine -> A B C D E F Dick 3. 5. 4. 1. 2. 6. Mike 4. 2. 3. 1. 6. 5. Bob 1. 5. 3. 6. 2. 4. Burt 5. 3. 1. 2. 4. 6. Ed 6. 2. 1. 4. 5. 3.
Table of Votes Against Wine -> A B C D E F
Group Ranking -> 4 3 1 2 4 6 Votes Against -> 19 17 12 14 19 24
( 5 is the best possible, 30 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 = 0.2046
The probability that random chance could be responsible for this correlation is rather large, 0.4021. 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 Burt 0.8986 Mike 0.2354 Dick 0.0857 Ed -0.0857 Bob -0.5429
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 C is Ch. Palmer 1997 2. ........ 2nd place Wine D is Ch, Margaux 1998 3. ........ 3rd place Wine B is Ch. Latour 1997 4. tied for 4th place Wine A is Ch. Cheval Blanc 1997 5. tied for 4th place Wine E is Ch. Latour 1998 --------------------------------------------------- 6. ........ 6th place Wine F is Ch. Haut Brion 1997 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 5.1143. The probability that this could happen by chance is 0.4021 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 0.89 for significance at the 0.05 level and must exceed 0.83 for significance at the 0.1 level Dick Mike Bob Dick 1.000 0.200 0.029 Mike 0.200 1.000 -0.714 Bob 0.029 -0.714 1.000 Burt 0.371 0.657 -0.371 Ed -0.543 0.371 -0.486 Burt Ed Dick 0.371 -0.543 Mike 0.657 0.371 Bob -0.371 -0.486 Burt 1.000 0.543 Ed 0.543 1.000 Pairwise correlations in descending order 0.657 Mike and Burt Not significant 0.543 Burt and Ed Not significant 0.371 Mike and Ed Not significant 0.371 Dick and Burt Not significant 0.200 Dick and Mike Not significant 0.029 Dick and Bob Not significant -0.371 Bob and Burt Not significant -0.486 Bob and Ed Not significant -0.543 Dick and Ed Not significant -0.714 Mike and Bob Not significant
COMMENT: The host hasn't tasted any of these wines in about five years and at that time he was not totally pleased with how they btasted. Today, they were much improved and on the whole they did taste like first growths or nearly that. The wines were quite similar and only the Haut Brion stood out as less than adequate. They were all enjoyable and ready to drink.
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