WINETASTER ON 03/07/11 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 Buiterverwachting Christine 1998 Constantia tied for 3rd place Wine B is Cordoba Crescendo 1998 Stellenbosch ........ 7th place Wine C is De Trafford 2000 Stellenbosch ........ 6th place Wine D is Thelema 1999 Stellenbosch ........ 5th place Wine E is Kanonkop Sauer 1999 Stellenbosch ........ 8th place Wine F is Groot Constantia Gouverneur's Reserve 1998 Constantia tied for 1st place Wine G is Rupert & Rothschild Baron Edmond 1999, Coastal Region tied for 3rd place Wine H is Meinert, Devon Valley 2000 Stellenbosch tied for 1st place
The Judges's Rankings
Judge Wine -> A B C D E F G H John 4. 8. 7. 3. 6. 2. 1. 5. Bob 1. 7. 8. 3. 4. 6. 2. 5. Orley 4. 6. 1. 7. 8. 3. 5. 2. Zaki 8. 4. 6. 5. 7. 3. 2. 1. Mike 5. 7. 6. 3. 8. 1. 4. 2. Burt 3. 2. 4. 5. 8. 1. 7. 6. Ed 5. 1. 2. 4. 8. 6. 7. 3. Dick 1. 6. 4. 2. 8. 7. 3. 5.
Table of Votes Against Wine -> A B C D E F G H
Group Ranking -> 3 7 6 5 8 1 3 1 Votes Against -> 31 41 38 32 57 29 31 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 = 0.2359
The probability that random chance could be responsible for this correlation is quite small, 0.0672. 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 Mike 0.6228 John 0.5030 Dick 0.1796 Bob 0.0482 Zaki 0.0238 Orley -0.0241 Burt -0.1677 Ed -0.2635
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 F is Groot Constantia Gouverneur's Reserve 1998 Constantia 2. tied for 1st place Wine H is Meinert Devon Valley 2000 Stellenbosch 3. tied for 3rd place Wine A is Buiterverwachting Christine 1998 Constantia 4. tied for 3rd place Wine G is Rupert & Rothschild Baron Edmond 1999, Coastal Region 5. ........ 5th place Wine D is Thelema 1999 Stellenbosch 6. ........ 6th place Wine C is De Trafford 2000 Stellenbosch 7. ........ 7th place Wine B is Cordoba Crescendo 1998 Stellenbosch --------------------------------------------------- 8. ........ 8th place Wine E is Kanonkop Sauer 1999 Stellenbosch We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 13.2083. The probability that this could happen by chance is 0.0672 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 John Bob Orley John 1.000 0.619 -0.024 Bob 0.619 1.000 -0.405 Orley -0.024 -0.405 1.000 Zaki 0.333 -0.190 0.286 Mike 0.690 0.119 0.429 Burt -0.095 -0.381 0.357 Ed -0.619 -0.595 0.405 Dick 0.333 0.571 0.143 Zaki Mike Burt John 0.333 0.690 -0.095 Bob -0.190 0.119 -0.381 Orley 0.286 0.429 0.357 Zaki 1.000 0.619 -0.048 Mike 0.619 1.000 0.262 Burt -0.048 0.262 1.000 Ed 0.119 -0.048 0.476 Dick -0.190 0.190 0.024 Ed Dick John -0.619 0.333 Bob -0.595 0.571 Orley 0.405 0.143 Zaki 0.119 -0.190 Mike -0.048 0.190 Burt 0.476 0.024 Ed 1.000 0.167 Dick 0.167 1.000 Pairwise correlations in descending order 0.690 John and Mike Significantly positive 0.619 Zaki and Mike Not significant 0.619 John and Bob Not significant 0.571 Bob and Dick Not significant 0.476 Burt and Ed Not significant 0.429 Orley and Mike Not significant 0.405 Orley and Ed Not significant 0.357 Orley and Burt Not significant 0.333 John and Dick Not significant 0.333 John and Zaki Not significant 0.286 Orley and Zaki Not significant 0.262 Mike and Burt Not significant 0.190 Mike and Dick Not significant 0.167 Ed and Dick Not significant 0.143 Orley and Dick Not significant 0.119 Zaki and Ed Not significant 0.119 Bob and Mike Not significant 0.024 Burt and Dick Not significant -0.024 John and Orley Not significant -0.048 Zaki and Burt Not significant -0.048 Mike and Ed Not significant -0.095 John and Burt Not significant -0.190 Bob and Zaki Not significant -0.190 Zaki and Dick Not significant -0.381 Bob and Burt Not significant -0.405 Bob and Orley Not significant -0.595 Bob and Ed Not significant -0.619 John and Ed Not significant
COMMENT: One of the tasters felt that the wines lacked significant bouquets, while another felt that a distinct hint of eucalyptus was present in a number of the wines. Everyone thought that the wines, with one exception, had developed nicely and were delicious to drink now. The Kanonkop was considered flawed by many of the tasters. The flawed Kanonkop may not be representative of other bottles of this wine. Our host felt that, having tasted the wines individually previously, taken as a group the wines seemed sweeter and less acidic. With the exception of the flawed wine there was remarkable agreement among the tasters about the quality of the remaining seven wines which were extraordinarily delicious to drink. (Note that the p-value of the W copefficient was 0.067, i.e., almost significant at the 0.05 level.) No significant vintage effects were seen. We can test the sum of ranksums for each year against the sum over the remaining two years (ignoring the complication that three such tests are not independent of one another) and none of these tests has a significant result, not even testing the year 2000 against the other two, which superficially seems to promise most in terms of significance.
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