WINETASTER ON 05/21/21 WITH 8 JUDGES AND 5 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2021 Richard E. Quandt, V. 1.65

A Vertical Tastintg of Dunn Howell Mountain

FLIGHT 1: Number of Judges = 8 Number of Wines = 5

Identification of the Wine: The judges' overall ranking:

Wine A is 1994 ........ 4th place Wine B is 1992 ........ 5th place Wine C is 1996 ........ 2nd place Wine D is 1990 ........ 3rd place Wine E is 1988 ........ 1st place

The Judges's Rankings

Judge Wine -> A B C D E Dick 1. 5. 4. 3. 2. Zaki 3. 4. 1. 5. 2. Bob 4. 1. 5. 3. 2. Burt 5. 4. 2. 3. 1. Frank 4. 5. 3. 1. 2. Orley 4. 5. 1. 2. 3. Ed 5. 2. 4. 3. 1. Peter 2. 5. 3. 4. 1.

Table of Votes Against Wine -> A B C D E

Group Ranking -> 4 5 2 3 1 Votes Against -> 28 31 23 24 14

( 8 is the best possible, 40 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 = 0.2594

The probability that random chance could be responsible for this correlation is quite small, 0.0812. 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 Correlation Price Burt 0.8721 -0.6000 Frank 0.7000 -0.2000 Orley 0.6669 0.2000 Peter 0.5270 0.0000 Ed 0.3000 -1.0000 Zaki 0.2000 0.1000 Dick -0.1000 0.3000 Bob -0.3000 -0.8000

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 E is 1988 --------------------------------------------------- 2. ........ 2nd place Wine C is 1996 3. ........ 3rd place Wine D is 1990 4. ........ 4th place Wine A is 1994 --------------------------------------------------- 5. ........ 5th place Wine B is 1992 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 8.3000. The probability that this could happen by chance is 0.0812

We now test whether the group ranking of wines is correlated with the prices of the wines. The rank correlation between them is -0.3000. At the 10% level of significance this would have to exceed the critical value of 0.8000 to be significant.

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 0.90 for significance at the 0.1 level Dick Zaki Bob Dick 1.000 0.100 -0.300 Zaki 0.100 1.000 -0.500 Bob -0.300 -0.500 1.000 Burt -0.100 0.500 0.000 Frank 0.300 -0.100 -0.200 Orley 0.000 0.400 -0.700 Ed -0.300 -0.100 0.800 Peter 0.800 0.600 -0.300 Burt Frank Orley Dick -0.100 0.300 0.000 Zaki 0.500 -0.100 0.400 Bob 0.000 -0.200 -0.700 Burt 1.000 0.600 0.600 Frank 0.600 1.000 0.700 Orley 0.600 0.700 1.000 Ed 0.600 0.200 -0.200 Peter 0.400 0.300 0.200 Ed Peter Dick -0.300 0.800 Zaki -0.100 0.600 Bob 0.800 -0.300 Burt 0.600 0.400 Frank 0.200 0.300 Orley -0.200 0.200 Ed 1.000 0.000 Peter 0.000 1.000 Pairwise correlations in descending order 0.800 Dick and Peter Not significant 0.800 Bob and Ed Not significant 0.700 Frank and Orley Not significant 0.600 Zaki and Peter Not significant 0.600 Burt and Frank Not significant 0.600 Burt and Orley Not significant 0.600 Burt and Ed Not significant 0.500 Zaki and Burt Not significant 0.400 Burt and Peter Not significant 0.400 Zaki and Orley Not significant 0.300 Dick and Frank Not significant 0.300 Frank and Peter Not significant 0.200 Frank and Ed Not significant 0.200 Orley and Peter Not significant 0.100 Dick and Zaki Not significant 0.000 Dick and Orley Not significant 0.000 Ed and Peter Not significant 0.000 Bob and Burt Not significant -0.100 Zaki and Ed Not significant -0.100 Dick and Burt Not significant -0.100 Zaki and Frank Not significant -0.200 Orley and Ed Not significant -0.200 Bob and Frank Not significant -0.300 Dick and Bob Not significant -0.300 Bob and Peter Not significant -0.300 Dick and Ed Not significant -0.500 Zaki and Bob Not significant -0.700 Bob and Orley Not significant

COMMENT: This was the first occasion since the pandemic began that we all attended in person in the lovely garden bower of one of our members. This was a great joy to all attendees. The wines were delicious and there was noticeable agreement in the group. It was interesting that the oldest wine was the favorite of the group/ These wines clearly age well. The two most expensive wines were the group's least favorite. Four members had a negative correlation with the pridce and only one member had a substantial positive correlation with the price. In any event, the wines were delicious.

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