WINETASTER ON 5/6/95 WITH 8 JUDGES AND 10 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 = 10
Identification of the Wine: The judges' overall ranking:
Wine A is Dunn Napa 1982 ........ 10th place Wine B is Dunn Napa 1983 ........ 9th place Wine C is Dunn Napa 1984 ........ 2nd place Wine D is Dunn Napa 1985 ........ 3rd place Wine E is Dunn Napa 1986 ........ 4th place Wine F is Dunn Howell Mountain 1986 ........ 1st place Wine G is Dunn Napa 1987 ........ 5th place Wine H is Dunn Howell Mountain 1988 ........ 7th place Wine I is Dunn Howell Mountain 1989 ........ 8th place Wine J is Dunn Howell Mountain 1990 ........ 6th place
The Judges's Rankings
Judge Wine -> A B C D E F G H I J Ken 7. 9. 5. 1. 10. 2. 3. 4. 6. 8. Burt 8. 9. 6. 10. 1. 3. 7. 4. 2. 5. Bob 10. 8. 5. 6. 1. 3. 9. 7. 4. 2. Orley 1. 2. 3. 7. 5. 4. 6. 8. 10. 9. Ed 10. 8. 3. 2. 5. 4. 6. 9. 7. 1. Frank 6. 7. 2. 4. 5. 3. 1. 8. 9. 10. John 8. 2. 3. 5. 7. 1. 9. 4. 10. 6. Dick 10. 9. 8. 5. 7. 6. 1. 3. 4. 2.
Table of Votes Against Wine -> A B C D E F G H I J
Group Ranking -> 10 9 2 3 4 1 5 7 8 6 Votes Against -> 60 54 35 40 41 26 42 47 52 43
( 8 is the best possible, 80 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 = 0.1636
The probability that random chance could be responsible for this correlation is rather large, 0.2259. 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 Ed 0.5061 Frank 0.2561 Bob 0.2371 Ken 0.2128 John 0.2128 Dick 0.0729 Burt -0.0061 Orley -0.1337
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 F is Dunn Howell Mountain 1986 --------------------------------------------------- 2. ........ 2nd place Wine C is Dunn Napa 1984 3. ........ 3rd place Wine D is Dunn Napa 1985 4. ........ 4th place Wine E is Dunn Napa 1986 5. ........ 5th place Wine G is Dunn Napa 1987 6. ........ 6th place Wine J is Dunn Howell Mountain 1990 7. ........ 7th place Wine H is Dunn Howell Mountain 1988 8. ........ 8th place Wine I is Dunn Howell Mountain 1989 9. ........ 9th place Wine B is Dunn Napa 1983 --------------------------------------------------- 10. ........ 10th place Wine A is Dunn Napa 1982 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 11.7818. The probability that this could happen by chance is 0.2259 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 0.65 for significance at the 0.05 level and must exceed 0.56 for significance at the 0.1 level Ken Burt Bob Ken 1.000 -0.248 -0.224 Burt -0.248 1.000 0.709 Bob -0.224 0.709 1.000 Orley -0.188 -0.394 -0.418 Ed 0.224 0.018 0.636 Frank 0.503 -0.224 -0.212 John 0.176 -0.164 0.115 Dick 0.370 0.224 0.176 Orley Ed Frank Ken -0.188 0.224 0.503 Burt -0.394 0.018 -0.224 Bob -0.418 0.636 -0.212 Orley 1.000 -0.309 0.467 Ed -0.309 1.000 0.188 Frank 0.467 0.188 1.000 John 0.394 0.212 0.176 Dick -0.830 0.309 -0.115 John Dick Ken 0.176 0.370 Burt -0.164 0.224 Bob 0.115 0.176 Orley 0.394 -0.830 Ed 0.212 0.309 Frank 0.176 -0.115 John 1.000 -0.333 Dick -0.333 1.000 Pairwise correlations in descending order 0.709 Burt and Bob Significantly positive 0.636 Bob and Ed Significantly positive 0.503 Ken and Frank Not significant 0.467 Orley and Frank Not significant 0.394 Orley and John Not significant 0.370 Ken and Dick Not significant 0.309 Ed and Dick Not significant 0.224 Burt and Dick Not significant 0.224 Ken and Ed Not significant 0.212 Ed and John Not significant 0.188 Ed and Frank Not significant 0.176 Frank and John Not significant 0.176 Bob and Dick Not significant 0.176 Ken and John Not significant 0.115 Bob and John Not significant 0.018 Burt and Ed Not significant -0.115 Frank and Dick Not significant -0.164 Burt and John Not significant -0.188 Ken and Orley Not significant -0.212 Bob and Frank Not significant -0.224 Ken and Bob Not significant -0.224 Burt and Frank Not significant -0.248 Ken and Burt Not significant -0.309 Orley and Ed Not significant -0.333 John and Dick Not significant -0.394 Burt and Orley Not significant -0.418 Bob and Orley Not significant -0.830 Orley and Dick Significantly negative
COMMENT: The agreement about the ranking of wines was weak. A comparison of the rank totals for the Napa wines and the Howell Mountain wines respectively (a questionable comparison to begin with, because the vintages are not matched) show no significant difference.
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