WINETASTER ON 4/10/95 WITH 8 JUDGES AND 8 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2011 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 8 Number of Wines = 8
Identification of the Wine: The judges' overall ranking:
Wine A is Torres Gran Coronas Res. Black Label 1976 ........ 8th place Wine B is 1973 tied for 1st place Wine C is 1975 ........ 6th place Wine D is 1983 ........ 4th place Wine E is 1970 ........ 7th place Wine F is 1982 ........ 3rd place Wine G is 1971 ........ 5th place Wine H is 1977 tied for 1st place
The Judges's Rankings
Judge Wine -> A B C D E F G H Dick 7. 1. 8. 4. 3. 2. 6. 5. Orley 8. 1. 5. 4. 6. 7. 3. 2. Ed 8. 7. 4. 1. 6. 5. 3. 2. Ken 6. 8. 5. 7. 3. 4. 1. 2. Bob 3. 1. 2. 6. 8. 4. 5. 7. Frank 5. 6. 7. 2. 8. 4. 3. 1. Burt 6. 4. 2. 5. 3. 1. 7. 8. John 5. 1. 4. 6. 3. 7. 8. 2.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 8 1 6 4 7 3 5 1 Votes Against -> 48 29 37 35 40 34 36 29
( 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 = 0.0982
The probability that random chance could be responsible for this correlation is rather large, 0.5992. 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 Orley 0.4671 Ed 0.1205 Dick 0.0476 John -0.0482 Frank -0.0723 Bob -0.1905 Ken -0.3095 Burt -0.4524
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 B is 1973 2. tied for 1st place Wine H is 1977 3. ........ 3rd place Wine F is 1982 4. ........ 4th place Wine D is 1983 5. ........ 5th place Wine G is 1971 6. ........ 6th place Wine C is 1975 7. ........ 7th place Wine E is 1970 --------------------------------------------------- 8. ........ 8th place Wine A is Torres Gran Coronas Res. Black Label 1976 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 5.5000. The probability that this could happen by chance is 0.5992 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 Dick Orley Ed Dick 1.000 0.262 -0.167 Orley 0.262 1.000 0.405 Ed -0.167 0.405 1.000 Ken -0.262 0.000 0.333 Bob -0.071 0.048 -0.476 Frank -0.048 0.333 0.690 Burt 0.310 -0.429 -0.310 John 0.262 0.429 -0.286 Ken Bob Frank Dick -0.262 -0.071 -0.048 Orley 0.000 0.048 0.333 Ed 0.333 -0.476 0.690 Ken 1.000 -0.595 0.238 Bob -0.595 1.000 -0.310 Frank 0.238 -0.310 1.000 Burt -0.310 0.310 -0.643 John -0.310 0.095 -0.310 Burt John Dick 0.310 0.262 Orley -0.429 0.429 Ed -0.310 -0.286 Ken -0.310 -0.310 Bob 0.310 0.095 Frank -0.643 -0.310 Burt 1.000 -0.048 John -0.048 1.000 Pairwise correlations in descending order 0.690 Ed and Frank Significantly positive 0.429 Orley and John Not significant 0.405 Orley and Ed Not significant 0.333 Orley and Frank Not significant 0.333 Ed and Ken Not significant 0.310 Bob and Burt Not significant 0.310 Dick and Burt Not significant 0.262 Dick and Orley Not significant 0.262 Dick and John Not significant 0.238 Ken and Frank Not significant 0.095 Bob and John Not significant 0.048 Orley and Bob Not significant 0.000 Orley and Ken Not significant -0.048 Burt and John Not significant -0.048 Dick and Frank Not significant -0.071 Dick and Bob Not significant -0.167 Dick and Ed Not significant -0.262 Dick and Ken Not significant -0.286 Ed and John Not significant -0.310 Ken and John Not significant -0.310 Ed and Burt Not significant -0.310 Ken and Burt Not significant -0.310 Bob and Frank Not significant -0.310 Frank and John Not significant -0.429 Orley and Burt Not significant -0.476 Ed and Bob Not significant -0.595 Ken and Bob Not significant -0.643 Frank and Burt Not significant
COMMENT: The 1976 was thought to be significantly worse than the other wines. 1976 was characterized by a cool, rainy spring and a warm, sunny summer.
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