WINETASTER ON 10/01/07 WITH 5 JUDGES AND 4 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2007 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 5 Number of Wines = 4
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Haut Brion 1990 ........ 3rd place Wine B is Ch. Haut Brion 1989 ........ 2nd place Wine C is Ch. Palmer 1990 ........ 1st place Wine D is Ch. Palmer 1989 ........ 4th place
The Judges's Rankings
Judge Wine -> A B C D Mike 3. 2. 1. 4. Frank 2. 1. 3. 4. Orley 3. 2. 1. 4. Burt 2. 4. 1. 3. Dick 3. 1. 2. 4.
Table of Votes Against Wine -> A B C D
Group Ranking -> 3 2 1 4 Votes Against -> 13 10 8 19
( 5 is the best possible, 20 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 = 0.5520
The probability that random chance could be responsible for this correlation is quite small, 0.0406. 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 Correlation Price Mike 1.0000 0.3162 Orley 1.0000 0.3162 Dick 0.8000 -0.2108 Frank 0.4000 -0.7379 Burt -0.2000 0.6325
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 1990 2. ........ 2nd place Wine B is Ch. Haut Brion 1989 3. ........ 3rd place Wine A is Ch. Haut Brion 1990 --------------------------------------------------- 4. ........ 4th place Wine D is Ch. Palmer 1989 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 8.2800. The probability that this could happen by chance is 0.0406
We now test whether the group ranking of wines is correlated with the prices of the wines. The rank correlation between them is 0.3162. At the 10% level of significance this would have to exceed the critical value of 1.0000 to be significant.
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 Mike Frank Orley Mike 1.000 0.400 1.000 Frank 0.400 1.000 0.400 Orley 1.000 0.400 1.000 Burt 0.400 -0.400 0.400 Dick 0.800 0.800 0.800 Burt Dick Mike 0.400 0.800 Frank -0.400 0.800 Orley 0.400 0.800 Burt 1.000 -0.200 Dick -0.200 1.000 Pairwise correlations in descending order 1.000 Mike and Orley Significantly positive 0.800 Frank and Dick Not significant 0.800 Orley and Dick Not significant 0.800 Mike and Dick Not significant 0.400 Mike and Frank Not significant 0.400 Orley and Burt Not significant 0.400 Mike and Burt Not significant 0.400 Frank and Orley Not significant -0.200 Burt and Dick Not significant -0.400 Frank and Burt Not significant
COMMENT: All of the wines were really quite excellent. As we say in British horse racing, there was little to choose among them. The tasting proves that these wines are now approachable, soft and ready to drink. In this tasting we had the incredibly famous 1989 Haut Brion. We thought it was good and hung right in the pack. This says to us that the 1990 Palmer could be a great buy. Of course, 1989 and 1990 are two of the truly remarkable vintages of the two decades.
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