WINETASTER ON 02/02/09 WITH 6 JUDGES AND 5 WINES BASED ON RANKS, IDENT=Y Copyright (c) 1995-2009 Richard E. Quandt, V. 1.65

FLIGHT 1: Number of Judges = 6 Number of Wines = 5

Identification of the Wine: The judges' overall ranking:

Wine A is Henschke Hill of Grace 1985 ........ 5th place Wine B is Henschke Hill of Grace 1986 ........ 3rd place Wine C is Henschke Hill of Grace 1987 tied for 1st place Wine D is Henschke Hill of Grace 1988 ........ 4th place Wine E is Henschke Hill of Grace 1989 tied for 1st place

The Judges's Rankings

Judge Wine -> A B C D E John 5. 3. 4. 2. 1. Burt 4. 5. 2. 3. 1. Orley 4. 3. 2. 5. 1. Bob 5. 2. 1. 4. 3. Mike 5. 3. 1. 4. 2. Dick 5. 2. 1. 4. 3.

Table of Votes Against Wine -> A B C D E

Group Ranking -> 5 3 1 4 1 Votes Against -> 28 18 11 22 11

( 6 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 = 0.5944

The probability that random chance could be responsible for this correlation is quite small, 0.0065. 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 Correlation I Mike 0.9000 1.0000 Orley 0.8000 1.0000 Bob 0.7000 1.0000 Dick 0.7000 1.0000 Burt 0.6000 1.0000 John 0.3000 1.0000

Next, we show the correlation among the wine identifications of the judges, which also ranges between 1.0 and 0.0:

C = 1.0000

The probability that random chance could be responsible for this correlation is rather large: > 10%. 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 C is Henschke Hill of Grace 1987 2. tied for 1st place Wine E is Henschke Hill of Grace 1989 --------------------------------------------------- 3. ........ 3rd place Wine B is Henschke Hill of Grace 1986 4. ........ 4th place Wine D is Henschke Hill of Grace 1988 --------------------------------------------------- 5. ........ 5th place Wine A is Henschke Hill of Grace 1985 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 14.2667. The probability that this could happen by chance is 0.0065 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 0.90 for significance at the 0.1 level John Burt Orley John 1.000 0.500 0.300 Burt 0.500 1.000 0.600 Orley 0.300 0.600 1.000 Bob 0.100 0.200 0.600 Mike 0.300 0.600 0.800 Dick 0.100 0.200 0.600 Bob Mike Dick John 0.100 0.300 0.100 Burt 0.200 0.600 0.200 Orley 0.600 0.800 0.600 Bob 1.000 0.900 1.000 Mike 0.900 1.000 0.900 Dick 1.000 0.900 1.000 Pairwise correlations in descending order 1.000 Bob and Dick Significantly positive 0.900 Bob and Mike Significantly positive 0.900 Mike and Dick Significantly positive 0.800 Orley and Mike Not significant 0.600 Orley and Dick Not significant 0.600 Burt and Mike Not significant 0.600 Orley and Bob Not significant 0.600 Burt and Orley Not significant 0.500 John and Burt Not significant 0.300 John and Orley Not significant 0.300 John and Mike Not significant 0.200 Burt and Dick Not significant 0.200 Burt and Bob Not significant 0.100 John and Bob Not significant 0.100 John and Dick Not significant

COMMENT: The Henschke "Hill of Grace" are among the most famous wines of Australia. They now sell at prices comparable to Penfold's Grange. These wines were purchased in Australia in the 1990s from several fine faculty club winelists. These wines were double decanted and needed it badly because they con- tained a lot of sediment. Also, the corks were typical of Australian wines of this period, i.e., short, and difficult to remove. There was overwhelming agreement among the tasters. The wines have an incredibly consistent style. For Australian wines made from the Shiraz grape they are very restrained in style, and have much more in common with the wines of the Northern Rhone than some would expect. They were all wonderful wines and justified their prices.

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