WINETASTER ON 01/04/10 WITH 6 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2003 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 6 Number of Wines = 8
Identification of the Wine: The judges' overall ranking:
Wine A is Robert Mondavi 1966 ........ 4th place Wine B is Souverain 1966 tied for 5th place Wine C is Louis Martini 1965 tied for 2nd place Wine D is Louis Martini 1963A tied for 2nd place Wine E is Diamond Creek ???? ........ 1st place Wine F is Louis Martini 1963B ........ 8th place Wine G is Concannon 1968 tied for 5th place Wine H is Charles Krug 1960 ........ 7th place
The Judges's Rankings
Judge Wine -> A B C D E F G H John 2. 7. 1. 3. 4. 8. 6. 5. Bob 5. 1. 3. 4. 2. 8. 7. 6. Mike 8. 5. 2. 3. 1. 7. 4. 6. Greg 5. 7. 1. 3. 2. 8. 6. 4. Burt 3. 2. 6. 1. 4. 8. 5. 7. Dick 2. 7. 6. 5. 3. 8. 1. 4.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 4 5 2 2 1 8 5 7 Votes Against -> 25 29 19 19 16 47 29 32
( 6 is the best possible, 48 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 = 0.4537
The probability that random chance could be responsible for this correlation is quite small, 0.0080. 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 Greg 0.7619 Mike 0.6467 John 0.5270 Bob 0.4524 Burt 0.3333 Dick 0.0241
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 E is Diamond Creek ???? --------------------------------------------------- 2. tied for 2nd place Wine D is Louis Martini 1963A 3. tied for 2nd place Wine C is Louis Martini 1965 4. ........ 4th place Wine A is Robert Mondavi 1966 5. tied for 5th place Wine B is Souverain 1966 6. tied for 5th place Wine G is Concannon 1968 7. ........ 7th place Wine H is Charles Krug 1960 --------------------------------------------------- 8. ........ 8th place Wine F is Louis Martini 1963B We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 19.0556. The probability that this could happen by chance is 0.0080 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 John Bob Mike John 1.000 0.333 0.333 Bob 0.333 1.000 0.548 Mike 0.333 0.548 1.000 Greg 0.833 0.452 0.714 Burt 0.286 0.619 0.214 Dick 0.333 -0.143 0.071 Greg Burt Dick John 0.833 0.286 0.333 Bob 0.452 0.619 -0.143 Mike 0.714 0.214 0.071 Greg 1.000 0.143 0.238 Burt 0.143 1.000 0.190 Dick 0.238 0.190 1.000 Pairwise correlations in descending order 0.833 John and Greg Significantly positive 0.714 Mike and Greg Significantly positive 0.619 Bob and Burt Not significant 0.548 Bob and Mike Not significant 0.452 Bob and Greg Not significant 0.333 John and Mike Not significant 0.333 John and Dick Not significant 0.333 John and Bob Not significant 0.286 John and Burt Not significant 0.238 Greg and Dick Not significant 0.214 Mike and Burt Not significant 0.190 Burt and Dick Not significant 0.143 Greg and Burt Not significant 0.071 Mike and Dick Not significant -0.143 Bob and Dick Not significant
Comments: It is amazing that these 40-50 year old wines were as good as they were. It is clear that these vineyards produced good and long-lasting wines; it is also clear that bottle variation is a very important factor, as witnessed by the two 1963 Martini wines (19 points against for one and 47 points against the other). It is also to be noted that California was making high-quality Cabernet Sauvignons before the 1976 "Judgment of Paris" and that happened to age as long as they did. But a fair question is how much longer these wines are likely to last. The agreement among the judges is very strong. Yet one may suspect that it is driven, at least in part, by the general dislike of one of the 1963 Louis Martini wines. As an exercise, without claiming statistical significance for this result, we reranked the wines as if wine F, the 1963 Martini that ranked lowest, did not exist. It turns out that the Kendall W coefficiant of concordance is now 0.2282, and the probability that this could have occurred by chance is 0.2228; hence this result is by no means significant. The Charles Krug, which was the 7th ranked wine before, is still 7th ranked and is now statistically "bad", which is not an unexpected result.
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