WINETASTER ON 04/11/11 WITH 8 JUDGES AND 8 WINES BASED ON RANKS, IDENT=Y Copyright (c) 1995-2011 Richard E. Quandt, V. 1.65

A Vertical Tasting of Château Latour

FLIGHT 1: Number of Judges = 8 Number of Wines = 8

Identification of the Wine: The judges' overall ranking:

Wine A is 1990 ........ 1st place Wine B is 2003 ........ 3rd place Wine C is 1995 ........ 4th place Wine D is 2002 ........ 2nd place Wine E is 1959 ........ 7th place Wine F is 1952 ........ 5th place Wine G is 1966 ........ 8th place Wine H is 1996 ........ 6th place

The Judges's Rankings

Judge Wine -> A B C D E F G H OPrley 7. 8. 1. 4. 3. 2. 5. 6. John 1. 3. 2. 4. 6. 5. 8. 7. Mike 1. 2. 4. 3. 6. 7. 8. 5. Ed 7. 6. 5. 2. 4. 3. 8. 1. Burt 2. 1. 7. 6. 3. 4. 8. 5. Bob 1. 4. 3. 2. 8. 6. 7. 5. Karl 2. 4. 5. 3. 6. 7. 8. 1. Dick 6. 3. 7. 4. 5. 2. 1. 8.

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

Group Ranking -> 1 3 4 2 7 5 8 6 Votes Against -> 27 31 34 28 41 36 53 38

( 8 is the best possible, 64 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 = 0.1830

The probability that random chance could be responsible for this correlation is rather large, 0.1748. 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 Bob 0.8193 0.0000 Mike 0.7306 0.0000 John 0.5988 0.0000 Karl 0.4458 0.0000 Burt 0.1905 0.0000 Ed -0.1317 0.0000 Dick -0.4762 0.0000 OPrley -0.5952 0.0000

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

C = 0.7500

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. ........ 1st place Wine A is 1990 2. ........ 2nd place Wine D is 2002 3. ........ 3rd place Wine B is 2003 4. ........ 4th place Wine C is 1995 5. ........ 5th place Wine F is 1952 6. ........ 6th place Wine H is 1996 7. ........ 7th place Wine E is 1959 --------------------------------------------------- 8. ........ 8th place Wine G is 1966 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 10.2500. The probability that this could happen by chance is 0.1748 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 0.74 for significance at the 0.05 level and must exceed 0.64 for significance at the 0.1 level OPrley John Mike OPrley 1.000 -0.071 -0.500 John -0.071 1.000 0.833 Mike -0.500 0.833 1.000 Ed 0.286 -0.214 -0.071 Burt -0.524 0.429 0.548 Bob -0.262 0.810 0.857 Karl -0.500 0.381 0.738 Dick -0.024 -0.310 -0.429 Ed Burt Bob OPrley 0.286 -0.524 -0.262 John -0.214 0.429 0.810 Mike -0.071 0.548 0.857 Ed 1.000 -0.048 -0.024 Burt -0.048 1.000 0.143 Bob -0.024 0.143 1.000 Karl 0.405 0.333 0.667 Dick -0.405 -0.071 -0.381 Karl Dick OPrley -0.500 -0.024 John 0.381 -0.310 Mike 0.738 -0.429 Ed 0.405 -0.405 Burt 0.333 -0.071 Bob 0.667 -0.381 Karl 1.000 -0.738 Dick -0.738 1.000 Pairwise correlations in descending order 0.857 Mike and Bob Significantly positive 0.833 John and Mike Significantly positive 0.810 John and Bob Significantly positive 0.738 Mike and Karl Significantly positive 0.667 Bob and Karl Significantly positive 0.548 Mike and Burt Not significant 0.429 John and Burt Not significant 0.405 Ed and Karl Not significant 0.381 John and Karl Not significant 0.333 Burt and Karl Not significant 0.286 OPrley and Ed Not significant 0.143 Burt and Bob Not significant -0.024 OPrley and Dick Not significant -0.024 Ed and Bob Not significant -0.048 Ed and Burt Not significant -0.071 Burt and Dick Not significant -0.071 OPrley and John Not significant -0.071 Mike and Ed Not significant -0.214 John and Ed Not significant -0.262 OPrley and Bob Not significant -0.310 John and Dick Not significant -0.381 Bob and Dick Not significant -0.405 Ed and Dick Not significant -0.429 Mike and Dick Not significant -0.500 OPrley and Mike Not significant -0.500 OPrley and Karl Not significant -0.524 OPrley and Burt Not significant -0.738 Karl and Dick Significantly negative

COMMENT: The wines were in excellent condition, including the wine that was almost 60 years old; there were subtle differences among them in acidity,the amount of tannin and fruit.Forced preference, which we use, by its nature highlights very small differences in terms of preference. In the case of these wines, which were very close to one another, this feature emphasizes the cost of rank ordering the wines rather than grading them. This subject is discussed in a recent and brilliant book by Michel Balinski and Rida Laraki,Majority Judgment: Measuring, Ranking, and Electing, MIT Press, 2011. For ordering the book, see amazon.com. An interesting question is whether the younger wines (1990 and later) are significantly different from the older ones (1966 and earlier). The Quandt statistic for testing the significance of the ratios of two ranksums (when divided by the number of ranksums in the numerator and denominator) is 1.3713 when the sum of the ranksums for the older wines is divided by the sum of the ranksums for the younger ones. The upper tail critical value is 1.2422; hence we can say with some confidence that the younger wines were deemed to taste better. It is worth mentioning in this connection that the three oldest wines, while in good bottle condition, did have considerable sediment and were decanted before the tasting. This might have something to do with their lower appeal. But overall, the quality of these wines underscores the lasting power of wines from this vineyard over 60+ years. All in all, this was an exceptional tasting.

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