WINETASTER ON 05/07/07 WITH 6 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2007 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 6 Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is G Mascarello Barolo Monprivato 2001 ........ 4th place Wine B is G Mascarello Barolo Monprivato 1997 ........ 1st place Wine C is G Mascarello Barolo Monprivato 1982 ........ 7th place Wine D is G Mascarello Barolo Monprivato 1998 ........ 5th place Wine E is G Mascarello Barolo Monprivato 1996 ........ 6th place Wine F is G Mascarello Barolo Monprivato 2000 ........ 3rd place Wine G is G Mascarello Barolo Monprivato 1999 ........ 2nd place
The Judges's Rankings
Judge Wine -> A B C D E F G Frank 5. 1. 7. 6. 4. 2. 3. Mike 1. 4. 7. 6. 3. 2. 5. Orley 4. 1. 7. 2. 5. 3. 6. Ed 5. 1. 7. 2. 6. 4. 3. Bob 4. 5. 7. 2. 6. 3. 1. Dick 2. 3. 4. 7. 5. 6. 1.
Table of Votes Against Wine -> A B C D E F G
Group Ranking -> 4 1 7 5 6 3 2 Votes Against -> 21 15 39 25 29 20 19
( 6 is the best possible, 42 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 = 0.3790
The probability that random chance could be responsible for this correlation is quite small, 0.0339. 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 Frank 0.7207 Ed 0.6736 Orley 0.3424 Bob 0.2728 Mike 0.1429 Dick -0.0360
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 B is G Mascarello Barolo Monprivato 1997 --------------------------------------------------- 2. ........ 2nd place Wine G is G Mascarello Barolo Monprivato 1999 3. ........ 3rd place Wine F is G Mascarello Barolo Monprivato 2000 4. ........ 4th place Wine A is G Mascarello Barolo Monprivato 2001 5. ........ 5th place Wine D is G Mascarello Barolo Monprivato 1998 6. ........ 6th place Wine E is G Mascarello Barolo Monprivato 1999 --------------------------------------------------- 7. ........ 7th place Wine C is G Mascarello Barolo Monprivato 1982 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 13.6429. The probability that this could happen by chance is 0.0339 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 0.79 for significance at the 0.05 level and must exceed 0.71 for significance at the 0.1 level Frank Mike Orley Frank 1.000 0.464 0.500 Mike 0.464 1.000 0.286 Orley 0.500 0.286 1.000 Ed 0.571 -0.036 0.786 Bob 0.250 0.071 0.250 Dick 0.214 0.143 -0.357 Ed Bob Dick Frank 0.571 0.250 0.214 Mike -0.036 0.071 0.143 Orley 0.786 0.250 -0.357 Ed 1.000 0.607 0.000 Bob 0.607 1.000 0.071 Dick 0.000 0.071 1.000 Pairwise correlations in descending order 0.786 Orley and Ed Significantly positive 0.607 Ed and Bob Not significant 0.571 Frank and Ed Not significant 0.500 Frank and Orley Not significant 0.464 Frank and Mike Not significant 0.286 Mike and Orley Not significant 0.250 Orley and Bob Not significant 0.250 Frank and Bob Not significant 0.214 Frank and Dick Not significant 0.143 Mike and Dick Not significant 0.071 Mike and Bob Not significant 0.071 Bob and Dick Not significant 0.000 Ed and Dick Not significant -0.036 Mike and Ed Not significant -0.357 Orley and Dick Not significant
COMMENT: These are wines made of the Nebbiolo grape, produced nowhere else in the world at this quality level. The wines have high natural acidity, uniformly high quality and, served with our loin of pork and fagioli salad, were delicious. If you eliminate C, you get a somewhat different picture of this tasting in that there is an enormously tight cluster of the other six wines. The overall W coefficient drops to 0.1619, which is not significant (the probability of a W as large or larger is 0.4336). One reason for this result is that wine C was considered by several tasters to be slightly oxidized. As a result, it certainly not surprising that it was ranked last by the group. The group wondered if we were to remove wine C whether or not we would have seen the correlation between the tasters that came through in this tasting, and the result is that it became much weaker. However, the overall group ranking did not change, except for the fact that wines F and G are now tied for second place.
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