WINETASTER ON 10/11/15 WITH 8 JUDGES AND 4 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-2015 Richard E. Quandt, V. 1.65
FLIGHT 1: Number of Judges = 8 Number of Wines = 4
Identification of the Wine: The judges' overall ranking:
Wine A is Lioco 2012 ........ 3rd place Wine B is Jay 2008 ........ 1st place Wine C is Hanzell 2011 ........ 4th place Wine D is Marimar Don Miguel 2012 ........ 2nd place
The Judges's Rankings
Judge Wine -> A B C D Lisa 3. 1. 4. 2. Dena 3. 2. 4. 1. Alan F 3. 1. 4. 2. Janet 2. 1. 4. 3. Alan K 3. 2. 4. 1. Mike 2. 1. 3. 4. Peter 1. 2. 4. 3. Julie 3. 2. 4. 1.
Table of Votes Against Wine -> A B C D
Group Ranking -> 3 1 4 2 Votes Against -> 20 12 31 17
( 8 is the best possible, 32 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 = 0.6062
The probability that random chance could be responsible for this correlation is quite small, 0.0022. 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 Lisa 1.0000 Alan F 1.0000 Dena 0.8000 Janet 0.8000 Alan K 0.8000 Julie 0.8000 Peter 0.4000 Mike 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 Jay 2008 --------------------------------------------------- 2. ........ 2nd place Wine D is Marimar Don Miguel 2012 3. ........ 3rd place Wine A is Lioco 2012 --------------------------------------------------- 4. ........ 4th place Wine C is Hanzell 2011 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 14.5500. The probability that this could happen by chance is 0.0022 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 Lisa Dena Alan F Lisa 1.000 0.800 1.000 Dena 0.800 1.000 0.800 Alan F 1.000 0.800 1.000 Janet 0.800 0.400 0.800 Alan K 0.800 1.000 0.800 Mike 0.400 -0.200 0.400 Peter 0.400 0.200 0.400 Julie 0.800 1.000 0.800 Janet Alan K Mike Lisa 0.800 0.800 0.400 Dena 0.400 1.000 -0.200 Alan F 0.800 0.800 0.400 Janet 1.000 0.400 0.800 Alan K 0.400 1.000 -0.200 Mike 0.800 -0.200 1.000 Peter 0.800 0.200 0.600 Julie 0.400 1.000 -0.200 Peter Julie Lisa 0.400 0.800 Dena 0.200 1.000 Alan F 0.400 0.800 Janet 0.800 0.400 Alan K 0.200 1.000 Mike 0.600 -0.200 Peter 1.000 0.200 Julie 0.200 1.000 Pairwise correlations in descending order 1.000 Alan K and Julie Significantly positive 1.000 Lisa and Alan F Significantly positive 1.000 Dena and Alan K Significantly positive 1.000 Dena and Julie Significantly positive 0.800 Lisa and Dena Not significant 0.800 Dena and Alan F Not significant 0.800 Lisa and Julie Not significant 0.800 Lisa and Alan K Not significant 0.800 Alan F and Alan K Not significant 0.800 Lisa and Janet Not significant 0.800 Alan F and Janet Not significant 0.800 Alan F and Julie Not significant 0.800 Janet and Mike Not significant 0.800 Janet and Peter Not significant 0.600 Mike and Peter Not significant 0.400 Alan F and Mike Not significant 0.400 Alan F and Peter Not significant 0.400 Dena and Janet Not significant 0.400 Janet and Alan K Not significant 0.400 Lisa and Peter Not significant 0.400 Lisa and Mike Not significant 0.400 Janet and Julie Not significant 0.200 Dena and Peter Not significant 0.200 Alan K and Peter Not significant 0.200 Peter and Julie Not significant -0.200 Alan K and Mike Not significant -0.200 Mike and Julie Not significant -0.200 Dena and Mike Not significant
COMMENT: The results are quite significant, which is unusual with such a small number of wines: Wine B turned out to be significantly good and C significantly bad.
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