Transcript Communicating Quantitative Information

Communicating Quantitative
Information
Midterms. Compound interest. Should you
guess on ….
Out-of-wedlock births (census data)
Jury selection.
Homework: Complete Project I (turn in proofread paper and/or 1 pager and be prepared to
present)
Election
• Latest www.fivethirtyeight.com
– Especially good on models of electorate,
confidence interval, spread
• VOTE
– Good thing to do for multiple reasons
• College loans issue, get the habit, other…
• Youth vote may be better than expectations…
– Extra credit
• Bring picture or some other evidence
Reprise: Excel
• Frequency calculation: sort data into bins,
count the number in each bin
• Named cells
• Various functions:
– median, average each take an array as
operand
– power: takes number and exponent
• Sort
– Note: we didn't do multiple columns
• Carry along or use for sorting
Preview: Excel
(where and when we do this will depend on time
required for presentations)
• Compound interest
– Aka time value of money
1000 grows to 1050 grows to (1050*1.05)…
1000
1050
1103
1158
1216
1276
1340
1407
Preview
• Mortgage on property (house)
• Borrow money according to some agreed upon
conditions
– Fixed interest rate, fixed amount of time (30 years)
– Floating interest rate, rate changes at fixed times
based on other rates
– Fixed rate for fixed time, then so-called balloon rate
• For all these, the bank has a lien on the house:
foreclosure on the house means that bank takes
over because payments were not made.
Sub prime mortgage
• People who were considered high risk (sub
prime borrowers) were given different conditions
– Higher rate
– Lower initial rate and then higher rate
– interest only and then so-called balloon payment
• Many of these loans have not been paid
• At some point, the loaners decide to give up
"Loans on the books"  Bad debts
– In place of a revenue stream, instead have property
that can be sold, but probably at lower prices and at a
cost in staffing…
Typical case (old days): Home
equity/second mortgage loan
• Person made substantial down payment (20%)
Say: $20,000 of $100,000 home.
• Prices / value of house (apparently) went up.
Suppose: 100,000 to 150,000
• As a consequence, owner still owed the bank,
but had increased equity. Say 20,000 + 50,000 +
5000 (paid off) = $75000
• Many people went to bank and borrowed against
this $75000! Used it for other bills.
– "using home as ATM"
Typical sales pitch
For original loans and for home
equity/second mortgages
• Houses are going up, so if the loan gets to
be too much, you can sell!
BUT what happens when smaller or zero
down payment AND/OR housing prices go
down?
Trade in mortgages
• A bank (loaner) can sell a mortgage to someone
else.
– I'm giving you the IOU from X. We agree on a price.
He now pays you.
• Securitized mortgages: Banks can and did
bundle mortgages and sell them to third parties
who sold shares in the mortgages to investors.
– This led to demand for more mortgages and less
oversight/interest in identifying good customers and
working with people in trouble.
– Who actually owns the mortgage? Who can
foreclose?
Next computer lab class
• Do original and second mortgage
examples.
• pmt (interest,numberpayments, principal)
– computes the payment to make, assuming
numberpayments constant payments, to pay
back a loan of principal amount at interest
– Each payment pays off some of the principal
plus the interest owed at that point.
– over time, more of the payment is towards the
principal and less covering the interest.
Should you guess …
• On my tests, yes, because I give partial
credit and I don't count off.
• But what about standardized tests: typical
formula is
penalty of ¼ for wrong answers
• Should you guess?
Answer
• Assume 5 multiple choice answers
• If you have no idea:
– What is the expected value of a guess?
1/5 of the time the value is 1
4/5 of the time the value is -1/4
– Total is 1/5 * 1 + 4/5 times (-1/4)
– Total is 0! On average, no benefit, but no
penalty from guessing.
Answer, continued
• What if you can remove one of the 5
answers, then expected value is
– ¼ of the time value 1
– ¾ of the time the value is -1/4
So total is ¼*1 + ¾* (-1/4) =
¼ = 4/16
¾* (-1/4) = -3/16
Total is 4/16 – 3/16 = 1/16.
This is positive, so it is worth guessing!
My conclusion
You should guess if
• guessing does not take too long
• … or get you too nervous
• you can remove 1 or 2 choices
Test strategy
• Study
• Practice taking practice tests, if available
• If you can rule out some of the answers
AND IT DOES NOT TAKE TOO LONG,
guess from remaining answers.
Out-of-wedlock births
• Fairly regular news story
• One or more populations have increases
in out-of-wedlock births
• As previous situations
– Definitions matter
– Must make note of issues and terms such as
percentages, rates, changing underlying
population, absolute vs rates, rates of change,
time interval under study
Challenge
• Let's pose some questions and see if we
can find answers.
http://www.cdc.gov/nchs/fastats/
unmarry.htm
• Unmarried Childbearing
• (Data are for U.S. in 2007)
• Number of live births to unmarried women:
1,715,047
• Birth rate for unmarried women: 52.3 births per
1,000 unmarried women aged 15-44 years
• Percent of all births to unmarried women: 39.7
• Source: Births, Final Data for 2007
Other source (story)
• http://www.acf.hhs.gov/programs/ofa/annu
alreport5/chap08.htm
– "Bonus to Reward Decrease in Illegitimacy
Ratio" to as many as five States (and three
Territories, if eligible) that achieve the largest
decrease in out-of-wedlock births without
experiencing an increase in their abortion
rates above 1995 levels.
Murphy Brown story
• TV character!!! choosing to have child as a
single mom. Criticized by VP Dan Quayle
• News story: Murphy Brown was accurate
Out-of-wedlock births by professional, welloff, non-minority women increasing at greater
rate than other groups.
– Be careful when comparing rates of change
– If 1% goes to 2%, this is a doubling,100% increase
– If 45% goes to 50%, this is increase of 11.1%
Jury selection
• From Cartoon Guide to Statistics.
• Based on real stories (may be
combination)
Notice
• Jury panel
– intended to be random selection of
• voting list
• driver's license?
• reachable at address
versus
• Jury
– dismissed for cause
– each side gets some number preemptory challenges:
chances to dismiss
– Attorneys use the jury selection process to
• find out about jury members
• begin to make their case
Jury panel
• Panel called up from voting lists (maybe other
lists as well)
• Juries are chosen from the panels.
• May be that previous (though not recent)
experience on jury makes it more likely that you
will be called
– I have served on local (Mt. Kisco), county (3 times),
federal (alternate), and federal grand jury
• Rules changed so not as easy to avoid service
• I RECOMMEND IT!
Case in textbook
• Area was 50% African-American, 50%
White in population.
• Panel consisted of 80 people, 4 AfricanAmerican.
• What is probability of such a panel if
selection was totally random?
• (What is the probability of flipping a fair
coin 80 times and only getting 4 heads?)
Calculation
• The TOTAL number of different strings of
heads/tails is 2 raised to the 80th power
– 2 * 2 * ……*2 (80 times)
• How many of these have exactly 4 heads?
• Heads can be anywhere in the string of
80.
• Let's take a detour and say the panel is
the size of the people in the class.
This class
• Random means at any time, any [student] can be picked
• What are the number of ways to pick exactly 3 males
when selecting a panel of 6?
– M M M F F F, M M F M FF, etc.
• The answer is: the same as choosing 3 places among
the 6
– 6 * 5 *4
– We’re not done—this is an overcount because it
counts M1 M2 M3 F F F and M2 M1 M3 F F F as
distinct, so need to divide by the number of ways you
can shuffle 3
– (6*5*4) / (3*2*1)
• (Note: this class is NOT half male and half female.)
Back to problem
• Write down all the patterns 80 long of
Heads and Tails (or some other
designation, e.g., W and A
• How many have exactly 4 A’s and all the
rest W?
Back to the problem
• 80 positions. Choosing which positions are
'Heads'
– Pick 4 from the 80: 80*79*78*77
– Divide by 4*3*2*1, because you don't care about
order of picking
• The total number is something less than 1/280
because once someone is chosen, then that
person is removed from the pool, so the ratio of
White to African-American changes slightly.
However, given a large population (>> 80), this
is a good estimate.
Calculation
• ((80*79*78*77)/(4*3*2*1))/(280)
• Using Excel as is OR
=binomdist(number,trials,probability,cumulative)
Answer is 1.30825E-18
This is 0.00000000000000000130825
Cartoon Book notes that this is less than the chances of
getting 3 royal flushes in a row in poker.
Judge ruled that it could not have been random and the court
had to change.
Alito story
• Riley v. Taylor
• Appeal found in favor of defense based on
statistical analysis on absence of AfricanAmericans on jury
– mis-use of pre-emptory challenges
• Alito dissented, saying only 10% of
Americans are left-handed and yet 5 of the
last 6 elected presidents are left-handed
Bush, Clinton, Bush Senior, Reagon, Carter, Ford
Counter-arguments
• Independent of statistics, there is a history of
racial bias
• Facts are wrong:
– Ford not elected. Nixon was right-handed
– Reagan and Bush, Jr also right handed
– So, of the last 6 elected, only 2 left-handed
• Wrong to stop at arbitrary point: of 43 presidents
(elected and not-elected), only 4 left-handed
– Note: left-handedness may not be reported accurately
• What do you think?
http://chance.dartmouth.edu/chancewiki/index.php/Cha
nce_News_9
Sub-groups
• Picking the last 6 presidents…
– You may pick the ones that suit your
argument by deciding when to stop.
• Recent Women's Health Initiative study,
discussion (disagreements) on findings of
sub-groups.
Homework
• Postings
• Complete Project 1
– essay (proofread!), charts and diagrams (at
least 1)
• Proof read ‘manually’ and
• Use spell and grammar check
– Ignore, ignore all when appropriate
– presentation (include 1 pager!!!)
• Proof read 1 pager AND charts
Themes
• What are the definitions?
• Is there any specialized language (jargon) here?
– Confidence level
• … out of what?
• What is the ‘universe’? What is the domain of
discussion?
• What is the context
– Time, space (geography)
– What else? If not this, what
• People who get medical treatment are [generally] sick, so
need to be compared to other sick people, not well-people!
• What else?
– What factors are not mentioned?
– Do things ‘add up’?