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This class discusses basic statistical inference topics in R, such as dataframes, graphical displays, data statistics, and sampling. It also examines the performance of financial experts compared to random stock choices and the psychic abilities of Paul the octopus.
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Mat 308 Topics in Statistical Inference Class 2, Thursday Aug 30
Objectives: learn basic commands in R: notion of dataframes, graphical displays of data, data statistics, sampling from data or distributions.
Can financial experts beat the darts? Starting in 1988, the Wall Street Journal run a contest between stocks chosen at randomly by Journal Staff members throwing darts at the Journal’s stock pages (mounted on a board) and stocks chosen by a team of 4 financial experts. At the end of 6 months, the Journal compared the percentage in the price of the experts’ stocks and the dartboard’s stocks. As of Nov. 23, 1998, the WSJ have had 101 overlapping six month contests. A new contest is started every month. The following data gives the percent gain for the average of the experts, the darts, and the Dow.http://www.dartmouth.edu/~chance/teaching_aids/data/darts_vs_experts.txt This dataset contains the results for the experts pics, the darts’ pics and the Dow. Which group performed better?
Individual activities • Read the dataset http://www.dartmouth.edu/~chance/teaching_aids/data/darts_vs_experts.txt and create numeric summaries for each group. • Display the 3 groups using comparative box plots and stripchart(filename[-1]), also try stripchart(filename[-1], method=“jitter”). Save your work.
Group activity: Which group performed better? Chose the one that applies best: • Financial experts clearly outperformed the Random choices • Financial experts clearly outperformed the Dow • Financial experts choices performed just as well as the Random choices • Financial experts choices performed worse than the Dow
Why was the Dow included? • Each group writes a sentence.
Group activity: Paul the octopus: is it psychic? • Read story in http://en.wikipedia.org/wiki/Paul_the_Octopus • Decide: Was Paul the octopus psychic? • Yes • No Give a rationale for your answer
Assume Paul was just a regular octopus with 50% chance of getting the answer right • Make 1000 simulations of choosing possible results for the 8 games if the selection was truly random, using the binomial distribution. • Represent the result of the 1000 simulations in one graph. • In your simulation, what was the probability of getting all 8 answers right?
Women loved Dr. Spock In 1969, the well-known pediatrician Dr. Benjamin Spock came to trial before a judge named Ford in Boston's Federal courthouse. He was charged with conspiracy to violate the Military Service Act (in addition to his work on child development he was active in anti-war protests in the 60s). A lawyer writing about the case that same year in the Chicago Law Review said about the case, "Of all defendants at such trials, Dr. Spock, who had given wise and welcome advice on child-bearing to millions of mothers, would have liked women on his jury."The jury was drawn from a panel of 350 persons, called a venire, selected by Judge Ford's clerk. This venire included only 102 women, even though 53% of the eligible jurors in the district were female. At the next stage in selecting the jury to hear the case, Judge Ford chose 100 potential jurors out of these 350 people. His choices included only 9 women.
Women loved Dr. Spock • panel of 350 persons • only 102 women in panel • If 350 people are chosen from all the eligible jurors in the district, how likely is it that the sample will include 102 women or fewer? Very likely (80%) About 50% Not so likely (<20%) Very unlikely (<1%) I can not decide Try: pbinom(350,.5,102)
Women loved Dr. Spock • Make 1000 simulations of choosing 100 people at random without replacement from a group of people consisting of 102 women and 248 men. • Display the result of the random simulation. Compute the proportion of cases in this simulation where the sample contained 9 women or fewer. Think about where in your picture falls the probability that the panel contains 9 women or fewer.
Women loved Dr. Spock • What do you conclude about the impartiality of Judge Ford's selection process? • It is clear that Judge Ford discriminated against choosing women for the panel. • Judge Ford was fair in choosing the panel
Assigned readings: • Bootstrapping.pdf • Chapter 3 pages 193-200 & Chapter 4 of Statistics: Unlocking the power of data • Chapter 3, sections 3.1-3.4 of Mathematical Statistics w/resampling and R.
