Communicating Quantitative Information

1
Communicating Quantitative Information

• Midterms. Compound interest. Should you guess on
  .
• Out-of-wedlock births (census data)
• Jury selection.
• Homework Complete Project I (turn in proof-read
  paper and/or 1 pager and be prepared to present)

2
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

3
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

4
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 (10501.05)

1000 1050 1103 1158 1216 1276 1340 1407
5
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.

6
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

7
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"

8
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?

9
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?

10
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.

11
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 ispenalty of ¼ for wrong answers
• Should you guess?

12
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.

13
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 -1/4So total is ¼1
  ¾ (-1/4) ¼ 4/16 ¾ (-1/4) -3/16Total
  is 4/16 3/16 1/16. This is positive, so it
  is worth guessing!

14
My conclusion

• You should guess if
• guessing does not take too long
• or get you too nervous
• you can remove 1 or 2 choices

15
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.

16
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

17
Challenge

• Let's pose some questions and see if we can find
  answers.

18
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

19
Other source (story)

• http//www.acf.hhs.gov/programs/ofa/annualreport5/
  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.

20
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,
  well-off, 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

21
Jury selection

• From Cartoon Guide to Statistics.
• Based on real stories (may be combination)

22
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

23
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!

24
Case in textbook

• Area was 50 African-American, 50 White in
  population.
• Panel consisted of 80 people, 4 African-American.
• 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?)

25
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.

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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
• Were not donethis 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
• (654) / (321)
• (Note this class is NOT half male and half
  female.)

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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 As and all the rest W?

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Back to the problem

• 80 positions. Choosing which positions are
  'Heads'
• Pick 4 from the 80 80797877
• Divide by 4321, 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 (gtgt 80), this is a good
  estimate.

29
Calculation

• ((80797877)/(4321))/(280)
• Using Excel as is ORbinomdist(number,trials,prob
  ability,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.

30
Alito story

• Riley v. Taylor
• Appeal found in favor of defense based on
  statistical analysis on absence of
  African-Americans 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

31
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/C
  hance_News_9

32
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.

33
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

34
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?