Presentation on theme: "Mat 308 Topics in Statistical Inference"— Presentation transcript:
1Mat 308 Topics in Statistical Inference Class 2, Thursday Aug 30
2Objectives:learn basic commands in R: notion of dataframes, graphical displays of data, data statistics, sampling from data or distributions.
3Can 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. This dataset contains the results for the experts pics, the darts’ pics and the Dow. Which group performed better?
4Individual activities Read the dataset 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.
5Group activity: Which group performed better? Chose the one that applies best:Financial experts clearly outperformed the Random choicesFinancial experts clearly outperformed the DowFinancial experts choices performed just as well as the Random choicesFinancial experts choices performed worse than the Dow
6Why was the Dow included? Each group writes a sentence.
7Group activity: Paul the octopus: is it psychic? Read story inDecide: Was Paul the octopus psychic?YesNoGive a rationale for your answer
8Assume 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?
9Women loved Dr. SpockIn 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.
10Women 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 decideTry: pbinom(350,.5,102)
11Women loved Dr. SpockMake 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.
12Women loved Dr. SpockWhat 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
13Assigned readings: Bootstrapping.pdf Chapter 3 pages & Chapter 4 of Statistics: Unlocking the power of dataChapter 3, sections of Mathematical Statistics w/resampling and R.