WINETASTER ON 6/8/93 WITH 7 JUDGES AND 4 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2011 Richard E. Quandt, V. 1.65
FLIGHT 2: Number of Judges = 7 Number of Wines = 4
Identification of the Wine: The judges' overall ranking:
Wine A is Ch. Pape Clement 1966 ........ 4th place Wine B is Ch. Margaux 1953 ........ 1st place Wine C is Ch. Trotanoy 1966 ........ 2nd place Wine D is Ch. Pape Clement 1959 ........ 3rd place
The Judges's Rankings
Judge Wine -> A B C D Peter 4. 1. 3. 2. Dick 4. 1. 2. 3. Grant 4. 1. 3. 2. Burt 3. 1. 2. 4. Frank 2. 1. 3. 4. Orley 3. 2. 1. 4. Rob 4. 1. 3. 2.
Table of Votes Against Wine -> A B C D
Group Ranking -> 4 1 2 3 Votes Against -> 24 8 17 21
( 7 is the best possible, 28 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 = 0.5918
The probability that random chance could be responsible for this correlation is quite small, 0.0061. 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 Dick 1.0000 Peter 0.8000 Grant 0.8000 Burt 0.8000 Rob 0.8000 Orley 0.6000 Frank 0.4000
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 Ch. Margaux 1953 --------------------------------------------------- 2. ........ 2nd place Wine C is Ch. Trotanoy 1966 3. ........ 3rd place Wine D is Ch. Pape Clement 1959 --------------------------------------------------- 4. ........ 4th place Wine A is Ch. Pape Clement 1966 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 12.4286. The probability that this could happen by chance is 0.0061 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 1.00 for significance at the 0.05 level and must exceed 1.00 for significance at the 0.1 level Peter Dick Grant Peter 1.000 0.800 1.000 Dick 0.800 1.000 0.800 Grant 1.000 0.800 1.000 Burt 0.400 0.800 0.400 Frank 0.200 0.400 0.200 Orley 0.000 0.600 0.000 Rob 1.000 0.800 1.000 Burt Frank Orley Peter 0.400 0.200 0.000 Dick 0.800 0.400 0.600 Grant 0.400 0.200 0.000 Burt 1.000 0.800 0.800 Frank 0.800 1.000 0.400 Orley 0.800 0.400 1.000 Rob 0.400 0.200 0.000 Rob Peter 1.000 Dick 0.800 Grant 1.000 Burt 0.400 Frank 0.200 Orley 0.000 Rob 1.000 Pairwise correlations in descending order 1.000 Peter and Rob Significantly positive 1.000 Peter and Grant Significantly positive 1.000 Grant and Rob Significantly positive 0.800 Peter and Dick Not significant 0.800 Dick and Burt Not significant 0.800 Burt and Orley Not significant 0.800 Dick and Grant Not significant 0.800 Burt and Frank Not significant 0.800 Dick and Rob Not significant 0.600 Dick and Orley Not significant 0.400 Frank and Orley Not significant 0.400 Dick and Frank Not significant 0.400 Burt and Rob Not significant 0.400 Peter and Burt Not significant 0.400 Grant and Burt Not significant 0.200 Peter and Frank Not significant 0.200 Frank and Rob Not significant 0.200 Grant and Frank Not significant 0.000 Grant and Orley Not significant 0.000 Peter and Orley Not significant 0.000 Orley and Rob Not significant
Comments: There was overwhelming agreement that the Margaux was the winner and the 1966 Pape Clement the loser, with the 1959 Pape Clement close behind the 1955, vying for the bottom position.
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