WINETASTER ON 12/29/99 WITH 7 JUDGES AND 5 WINES BASED ON RANKS, IDENT=N Copyright (c) 1995-99 Richard E. Quandt FLIGHT 1: Number of Judges = 7 Number of Wines = 5 Identification of the Wine: The judges' overall ranking: Wine A is J Phelbs,Cabernet,Napa 97 ........ 1st place Wine B is Sterling Vineyards,Cabernet,Napa 97 ........ 2nd place Wine C is R Mondavi,Cabernet,Coastal 97 ........ 3rd place Wine D is Undurraga Reserva,Maipo/Chile 96 ........ 4th place Wine E is R Mondavi,Cabernet, Napa 96 ........ 5th place The Judges's Rankings Judge Wine -> A B C D E Lisa 1. 2. 5. 3. 4. Nahomi 2. 1. 4. 3. 5. Gaby 1. 3. 4. 2. 5. Keith 2. 1. 4. 3. 5. Miwa 2. 3. 1. 4. 5. Alexander 1. 4. 2. 5. 3. Karl 1. 2. 3. 4. 5. Table of Votes Against Wine -> A B C D E Group Ranking -> 1 2 3 4 5 Votes Against -> 10 16 23 24 32 ( 7 is the best possible, 35 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 = 0.5714 The probability that random chance could be responsible for this correlation is quite small, 0.0030. 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 Karl 0.9747 Nahomi 0.8000 Keith 0.8000 Gaby 0.7000 Lisa 0.7000 Miwa 0.4000 Alexander 0.2000 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 A is J Phelbs,Cabernet,Napa 97 --------------------------------------------------- 2. ........ 2nd place Wine B is Sterling Vineyards,Cabernet,Napa 9 3. ........ 3rd place Wine C is R Mondavi,Cabernet,Coastal 97 4. ........ 4th place Wine D is Undurraga Reserva,Maipo/Chile 96 --------------------------------------------------- 5. ........ 5th place Wine E is R Mondavi,Cabernet, Napa 96 We now test whether the ranksums AS A WHOLE provide a significant ordering. The Friedman Chi-square value is 16.0000. The probability that this could happen by chance is 0.0030 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 Lisa Nahomi Gaby Lisa 1.000 0.800 0.800 Nahomi 0.800 1.000 0.700 Gaby 0.800 0.700 1.000 Keith 0.800 1.000 0.700 Miwa 0.000 0.300 0.300 Alexander 0.100 -0.100 0.100 Karl 0.700 0.800 0.700 Keith Miwa Alexander Lisa 0.800 0.000 0.100 Nahomi 1.000 0.300 -0.100 Gaby 0.700 0.300 0.100 Keith 1.000 0.300 -0.100 Miwa 0.300 1.000 0.600 Alexander -0.100 0.600 1.000 Karl 0.800 0.700 0.500 Karl Lisa 0.700 Nahomi 0.800 Gaby 0.700 Keith 0.800 Miwa 0.700 Alexander 0.500 Karl 1.000 Pairwise correlations in descending order 1.000 Nahomi and Keith Significantly positive 0.800 Lisa and Gaby Not significant 0.800 Lisa and Nahomi Not significant 0.800 Nahomi and Karl Not significant 0.800 Keith and Karl Not significant 0.800 Lisa and Keith Not significant 0.700 Gaby and Karl Not significant 0.700 Miwa and Karl Not significant 0.700 Nahomi and Gaby Not significant 0.700 Gaby and Keith Not significant 0.700 Lisa and Karl Not significant 0.600 Miwa and Alexander Not significant 0.500 Alexander and Karl Not significant 0.300 Nahomi and Miwa Not significant 0.300 Keith and Miwa Not significant 0.300 Gaby and Miwa Not significant 0.100 Lisa and Alexander Not significant 0.100 Gaby and Alexander Not significant 0.000 Lisa and Miwa Not significant -0.100 Nahomi and Alexander Not significant -0.100 Keith and Alexander Not significant COMMENT:Most of the judges were not expierenced in drinking wine let alone in doing wine tastings. Nevertheless everyone agrees that the Joseph Phelbs is an outstanding wine. The included supermarket-wine from Chile was considered to be the worst. The Mondavi Napa Cabernet was corked and should have been excluded from the tasting. Interesting is also a simple regression between ranking and price for the correlation seems to be almost perfect. The retailer prices were:
Joseph Phelbs: $31.39 Sterling Vineyards: $19.99 Mondavi Coastal: $ 8.99 Undurraga Reserva: $ 7.99 Mondavi Napa Valley:$23.29