We will walk through the statistics of life using some examples from Steven Levitts book on statistics and economics.
One example of the authors' use of economic theory involves demonstrating the existence of cheating among sumo wrestlers. In a sumo tournament, all wrestlers in the top division compete in 15 matches and face demotion if they do not win at least eight of them. The sumo community is very close-knit, and the wrestlers at the top levels tend to know each other well. The authors looked at the final match, and considered the case of a wrestler with seven wins, seven losses, and one fight to go, fighting against an 8-6 wrestler. Statistically, the 7-7 wrestler should have a slightly below even chance, since the 8-6 wrestler is slightly better. However, the 7-7 wrestler actually wins around 80% of the time. Levitt uses this statistic and other data gleaned from sumo wrestling matches, along with the effect that allegations of corruption have on match results, to conclude that those who already have 8 wins collude with those who are 7-7 and let them win, since they have already secured their position for the following tournament. Despite condemnation of the claims by the Japan Sumo Association following the book's publication in 2005, the 2011 Grand Tournament in Tokyo was cancelled for the first time since 1946 because of allegations of match fixing. The authors attempt to demonstrate the power of data mining, as a number of their results emerge from Levitt's analysis of various databases. The authors posit that various incentives encourage teachers to cheat by assisting their students with multiple-choice high-stakes tests. Such cheating in the Chicago school system is inferred from detailed analysis of students' answers to multiple choice questions. Levitt asks, "What would the pattern of answers look like if the teacher cheated?", and hypothesises that the more difficult questions found at the end of test sections will be answered correctly more frequently than the easy questions at the beginning of test sections.