Transcript Class02-08-30

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.tx
t
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:
A. Financial experts clearly outperformed the Random
choices
B. Financial experts clearly outperformed the Dow
C. Financial experts choices performed just as well as
the Random choices
D. 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_Octop
us
• Decide: Was Paul the octopus psychic?
A. Yes
B. 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?
A.
B.
C.
D.
E.
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?
A. It is clear that Judge Ford discriminated
against choosing women for the panel.
B. 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.