Communicating Quantitative Information

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Communicating Quantitative Information

  • News. Excel.
  • Adjuncts
  • Significant digits
  • Sports Records
  • Homework: Postings, plan project 2.


  • Payroll taxes: includes Social Security and Medicare. Also withholding (required paying in advance of income taxes)
    • system designed to make sure people pay. Typical occurrence is to get a refund.
  • Income taxes: calculated based on table. Includes standard or list of deductions. Progressive table. Marginal rate: rate (%) of amount over a certain amount.
    • mortgage interest deduction benefits richer people much more than middle class (1000s vs 100s) and poorer people not at all. BUT emotional argument may be too strong…..
  • Property taxes: based on real estate. Goes to local government, including schools, police, garbage, etc.
    • Different towns / counties / school districts / etc. have different systems of assessments.
  • Sales tax: formulas in different cities/towns/counties, on different types of goods.

In the news

  • Budget exercise: do as class
  • Big effects, small effects, effects over time.

In the news

  • General Motors stock offering
  • Background: 1.5 years ago, GM went bankrupt. Government takeover. Reorganized (dropped brands). Some of money goes to U.S. treasury, some to company. Government new stake will be 26% of company.

Excel problems

  • See email.
  • Time value of money
    • Money invested grows.
    • When comparing amounts of money at different points in time, money in the future is worth less now.
    • Different issue: comparing money at different times needs to adjust for inflation
      • ticket prices
      • college education
  • Learn how to / learn to use Help.


  • Definitions
    • Content/subject AND statistics
  • Denominator
  • What’s the difference? Context
    • Time, category, space, …
  • Dimension…of problem
  • Distribution
    • Mean or median information may not be enough

Too many adjunct professors?

  • Ongoing issue: recent article, then follow-up letters
  • Adjunct is part-timer teacher at college
  • Generally, money saver
    • Paid per course
    • Generally not paid for office hours, committee work, advising
      • Pay less, get less
  • But can be hired for unusual courses
    • Practicioner??
  • Often hired for lower-level courses….


  • Do you know if/when your teacher is an adjunct?
  • How many adjuncts have you had?

How to measure?

  • Adjuncts/all teachers
  • Courses taught by adjunct / all courses
  • Compute for each student, adjuncts/all teachers and then average over all students
    • OR do this for 1st year, or first 2 years
  • ????

Topic in news a few years ago

  • 50th Anniversary of Salk vaccine for polio
    • killed virus
    • Sabin vaccine: 'attenuated live virus', more common now (given orally)
  • Large double-blind test involving New York school children including me!
    • I (and others) get a new shot a year later because we were given placebos.
    • Success meant: fewer instances of polio in the condition group than in the placebo (aka control) group
  • Polio still significant problem in Asia and Africa

Topic in Mt. Kisco news

  • Village manager states that new policy is not to borrow unless expenditure is
    • over $100,000
    • capital expense
      • building and other long-lasting items
  • This means paying out of current budget (to be covered by current taxes and income)
  • Claim: this and other policies contributes to the village Moody's bond rating being A1
  • Comment?

Significant Digits

  • Measurements are limited to accuracy.
    • I am 62 inches tall (probably 61.5)
  • Ruler has markings. Meters have limits. Timers are limited (though getting better and better: a particular timer has a limit in precision.)
  • Computations with measurements must/should avoid reporting more digits than appropriate.


  • Measure height of several people with ruler with inch and tenth of inch markings
  • Report: 61.4, 64.0, 72.5, 73.8 (64.0 rather than 64 because you can distinguish between 64.0 and 64.1)
  • Computed average is 67.925. Report 67.9 because more would imply more precision than you can guarantee.


  • Set of rules for reporting, including report computed answer with no more significant digits than the least number in the operands
  • Must distinguish between measured quantities and 'pure numbers'—numbers with unlimited precision
  • Important to not round off too early: keep intermediate results at greater precision, do computation, and then round off.
  • Good sources found using google.


  • What should be reported as average for
    • 123.5 47.23
    • 64.548

Iraqi Dead May Total 600,000, Study Says

  • “It is the second study by researchers from the Johns Hopkins Bloomberg School of Public Health. It uses samples of casualties from Iraqi households to extrapolate an overall figure of 601,027 Iraqis dead from violence between March 2003 and July 2006.”
  • “But it is an estimate and not a precise count, and researchers acknowledged a margin of error that ranged from 426,369 to 793,663 deaths.”
  • Note: The headline: “Study estimates a minimum of 400,000 deaths” would have been newsworthy
  • Good headline by NYTimes


  • Nature of scales:
    • interval (measured, meaning to differences)
    • ordered
    • category (no order)
  • Tendency to report amounts to certain granularity: whole numbers, round off to 5 or 10, etc.

100m Men's World Record

  • Traditionally 'the world's fastest…'
  • Many studies

Changing precision

  • The precision possible in testing has improved from hand-held clocks to sensors for start and finish.
  • False start determination
    • False start has official definition: within some set amount of starting gun
  • Wind measurements for road races


  • Found using google: sports records
  • 100mm Sprinting: Is there a limit:

Look at newer records

  • Look at organization
    • pre-electronic timing
    • electronic timing
    • low altitude

Best (linear) fit

  • Formal definition of best linear fit:
  • Least squares:
  • Take distance from each actual point to line and square it. Add up. The line that minimizes this total is the best fit.

Reality check

  • Even though the best straight line through the points predicts a time of zero….that is not possible.
  • So, is there another way to frame the problem
  • Diversion: notion of limit (sometimes called asymptote)


  • (continuous) functions:
    • function f(x) tends (trends) to limit L as x goes to x0
    • formal definition: Specify how close you want function to get to L (say e distance), can find a value d such that if x is within d of xo, the distance of f(x) from L will be less than e.
  • (discrete) sequences, say years
    • function f(N) tends to limit L as N gets higher
    • formal definition: specify how close you want function to get to L (say e distance), can find a value N' such that if N>N', then the distance of f(N) from L is less than e
  • Usually given using Greek letters epsilon and delta and with absolute values.

Best logistic fit

  • Assume there is limit
  • Mathematical theory suggests that the logistic function is simplest curve
  • (logistic function has exponential term in denominator)

Reza D. Noubary (2005) "A Procedure for Prediction of Sports Records", Journal of Quantitative Analysis in Sports: Vol. 1: No. 1, Article 4.

Factors (all sports)

  • What can change trend? (these may overlap)
    • measurement procedures/policies
      • e.g., treatment of wind
    • equipment (shoes, track)
    • techniques
      • e.g., back stroke swimming
    • rules
      • e.g., traveling call in basketball
    • drugs (new inventions) and drug testing (absence of drugs)
    • ?
  • These can put records on a different trend line/curve

Factors in sports

  • Basic qualities
    • May be dependent on training
  • Technology
  • Technique
  • Tactics


  • Technology, technique, tactic???
  • Back stroke start
  • Pacing in long distance racing
  • backwards technique in jump
  • shoes, skiis, skates
  • fiber glass poles
  • swim suits
  • traditional versus skating cross-country skiing
    • This led to definition of two different events
  • ??


  • basketball
    • policy issue: 'traveling' rule not enforced as rigorously
  • baseball home runs
    • dependent on size of field
    • pitcher skill
    • policy issue: tactics used by pitchers (that is, can choose to walk anyone)


  • Changes in policies, technology, technique, tactics all put
  • "records on a different curve"

Sports articles

  • Teaching Statistics with Sports Examples
  • Wikipedia
  • Math Forum
  • Chance project (do a search on terms)


  • Project II
    • Post proposal and get approval!
  • Choice:
    • pick an actual newspaper/magazine and re-write it to be clearer. Include 1-3 'headlines' summarizing major points. Use diagrams, charts as appropriate.
    • pick topic/lesson from the class and write explanation(s) as newspaper story or regular essay. Use diagrams, charts as appropriate. Make up 'headlines' stating major points.
    • gapminder: pick 2 or 3 countries and do research to explain what led to changes in economics, health


  • Paper: informal presentation: 3-5 minute summary OR
  • Formal presentation
    • Charts using PowerPoint or something else
    • Prepare '1 pager': formal abstract, sources, 1 diagram or graph


  • References must be in standard format
    • Web addresses must contain: author (if available), organization, date given AND date viewed
  • Use bold, italics, capital letters to distinguish products, names, jargon, etc.
  • Use numerals for numbers > 3
  • Use tables when you want reader to compare sets of numbers
  • PROOFREAD: use Spell & grammar check AND re-read your own matter
    • its, it's
    • where, were
    • there, their, they're
    • your, you're
  • Plan presentation
    • plan way(s) to involve audience

Any paper/presentation

  • Do not list the facts from source 1, then source 2, then source 3.
  • Do synthesize
    • MAYBE list facts and then explain differences
    • Make your own conclusion
  • Remember
    • Definitions
    • Denominator: out of what
    • Distribution
    • What's the difference?


  • News stories postings
  • Project II proposal, project

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