Presentation on theme: "Communicating Quantitative Information Midterms. Compound interest. Should you guess on …. Out-of-wedlock births (census data) Jury selection. Homework:"— Presentation transcript:
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.comwww.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)… 10001050110311581216127613401407
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 2007Births, Final Data for 2007
Other source (story) http://www.acf.hhs.gov/programs/ofa/annu alreport5/chap08.htmhttp://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, 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 80 th 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 1/2 80 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))/(2 80 ) 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 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/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’?