John Emerson
Assistant Professor of Statistics
Yale University
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Congratulations to the gold medal winner! Bullet Points: The medals are correct. But under the rules, a computer would have awarded the silver to Slutskaya in just over 1/3 of all possible combinations of panels. According to 12 judges, Cohen deserved the silver and was fortunate in the selection of panels; Slutskaya was unlucky. Short Program: About 58% of the possible 220 panels would have placed Slutskaya over Cohen, and the consensus of all 12 judges would have placed Slutskaya ahead by 0.28 after the short program (the panel chosen by the computer had Cohen in front by 0.03). Judges 4, 5, and 9 were excluded by the computer. Free Skate: About 27% of the possible 220 panels would have placed Slutskaya ahead of Cohen, but the consensus of all 12 judges would have had Cohen ahead of Slutskaya by 0.91 (instead of the actual margin of 1.89). Judges 3, 9, and 12 were excluded by the computer. Final Standings: The 12 judges had Cohen in front of Slutskaya, by a margin of 0.63 points, so the medal standings are secure. A rough normal approximation indicates that about 30% of the panels of judges would have awarded Slutskaya the silver medal over Cohen. The exact figure: 16,295 of 48,400 combinations of panels would have awarded the silver to Slutskaya, just over 33% (and 132 possible panels would have created a tie between Slutskaya and Cohen). If you are wondering why this number is not the same as 0.58 times 0.27 (see the figures above), you have discovered a great question for a classroom of introductory statistics students. I'll use it myself. This is why I do what I do. |