WINETASTER ON 9/28/97 WITH 7 JUDGES AND 7 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2011 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 7 Number of Wines = 7
Identification of the Wine: The judges' overall ranking:
Wine A is Hermitage La Chappelle 1979 ........ 7th place Wine B is Hermitage La Chappelle 1982 ........ 1st place Wine C is Hermitage La Chappelle 1985 ........ 2nd place Wine D is Hermitage La Chappelle 1978 ........ 3rd place Wine E is Hermitage La Chappelle 1990 ........ 6th place Wine F is Hermitage La Chappelle 1983 ........ 5th place Wine G is Hermitage La Chappelle 1989 ........ 4th place
The Judges's Rankings
Judge Wine -> A B C D E F G John 7. 1. 2. 3. 5. 6. 4. Ed 7. 1. 6. 4. 3. 5. 2. Bob E 7. 1. 2. 5. 6. 3. 4. Orley 7. 1. 2. 3. 4. 6. 5. Stephen 3. 1. 2. 7. 6. 5. 4. Bob W 7. 1. 5. 4. 6. 3. 2. Dick 4. 6. 5. 1. 2. 3. 7.
Table of Votes Against Wine -> A B C D E F G
Group Ranking -> 7 1 2 3 6 5 4 Votes Against -> 42 12 24 27 32 31 28
( 7 is the best possible, 49 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 = 0.3601
The probability that random chance could be responsible for this correlation is quite small, 0.0193. 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 John 0.9550 Orley 0.8214 Bob E 0.7027 Bob W 0.5045 Ed 0.4144 Stephen 0.2342 Dick -0.5714
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 Hermitage La Chappelle 1982 --------------------------------------------------- 2. ........ 2nd place Wine C is Hermitage La Chappelle 1985 3. ........ 3rd place Wine D is Hermitage La Chappelle 1978 4. ........ 4th place Wine G is Hermitage La Chappelle 1989 5. ........ 5th place Wine F is Hermitage La Chappelle 1983 6. ........ 6th place Wine E is Hermitage La Chappelle 1990 --------------------------------------------------- 7. ........ 7th place Wine A is Hermitage La Chappelle 1979 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 15.1224. The probability that this could happen by chance is 0.0193 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 John Ed Bob E John 1.000 0.536 0.750 Ed 0.536 1.000 0.393 Bob E 0.750 0.393 1.000 Orley 0.964 0.500 0.679 Stephen 0.393 0.036 0.571 Bob W 0.571 0.750 0.750 Dick -0.321 -0.321 -0.500 Orley Stephen Bob W John 0.964 0.393 0.571 Ed 0.500 0.036 0.750 Bob E 0.679 0.571 0.750 Orley 1.000 0.321 0.429 Stephen 0.321 1.000 0.250 Bob W 0.429 0.250 1.000 Dick -0.143 -0.786 -0.500 Dick John -0.321 Ed -0.321 Bob E -0.500 Orley -0.143 Stephen -0.786 Bob W -0.500 Dick 1.000 Pairwise correlations in descending order 0.964 John and Orley Significantly positive 0.750 John and Bob E Significantly positive 0.750 Ed and Bob W Significantly positive 0.750 Bob E and Bob W Significantly positive 0.679 Bob E and Orley Not significant 0.571 Bob E and Stephen Not significant 0.571 John and Bob W Not significant 0.536 John and Ed Not significant 0.500 Ed and Orley Not significant 0.429 Orley and Bob W Not significant 0.393 John and Stephen Not significant 0.393 Ed and Bob E Not significant 0.321 Orley and Stephen Not significant 0.250 Stephen and Bob W Not significant 0.036 Ed and Stephen Not significant -0.143 Orley and Dick Not significant -0.321 Ed and Dick Not significant -0.321 John and Dick Not significant -0.500 Bob E and Dick Not significant -0.500 Bob W and Dick Not significant -0.786 Stephen and Dick Significantly negative
COMMENT: There was significant agreement in the group that the 1979 was of significantly low quality and the 1982 of significantly high quality. The most extensive comparison can be made between Report -2 and report -16. The following broad conclusions emerge from these. 1. In Report -2, ´82 is preferred to ´83, which in turn is preferred to ´79. 2. In Report -16, ´83 is preferred to 82 and ´79 is preferred to ´83. 3. ´79 is deemed worse than any other vintage in Report -2 but better than any other vintage in Report -16. 4. ´90 is preferred to ´83 in Report 40.
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