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)

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 ispenalty 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) = -3/16Total 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/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.

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%

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 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?)

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-18This 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 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

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/

Chance_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’?