Tonights Quantitative Thinking Presentation Theme TBA Later

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Tonights Quantitative Thinking Presentation
(Theme TBA Later)
There are three kinds of lies Lies, d______ed
lies, and statistics. attributed to Mark Twain

• Michael Hansen
• St. Albans School of Public Service
• Washington, DC
• June 29, 2006

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My background . . .

• Math and music (piano, violin, viola)
• M.S., Applied Mathematics, UIUC
• 19861998 U.S. Government contractor, primarily
  in the Pentagon
• 1998present STA math teacher

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Icebreaker Question

• In what city was I born? (Hint It is one of the
  ten largest cities in the U.S.)

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Your Backgrounds . . .

• Tell me something unusual that is not in your
  capsule bio

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Which of these subjects are you most likely to
use later in life?

• Geometry
• Algebra
• Statistics
• Calculus

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Why are geometry, algebra, and calculus taught in
high school?

• Goodness only knows.
• Life is cruel.
• Math teachers are greedy and want full
  employment.
• These subjects provide a chance to teach abstract
  reasoning skills.

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mortar brick glue

• stone
• wood
• water
• oil

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arachnid spider marsupial

• lizard
• kangaroo
• fish
• beetle

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What have we been doing here?

• Answer Gathering statistics.
• What is a statistic?
• A number computed from data.

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Which of these are examples of statistics?

• A batting average
• A vote tally for a political candidate
• A census (headcount) for a community
• A person who is injured in a traffic accident
• The statement, Most Americans support our troops
  in Iraq
• The statement, 51 of the adult voters polled
  stated that the war in Iraq has been a mistake
• The statement, 51 of adult American voters
  think the war in Iraq was a mistake

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Terms

• Data FACTS (plural) one fact is a datum
• Statistic a number computed from data
• Parameter a number that describes a population
• Key idea We use statistics to estimate
  parameters.
• Bias error in parameter estimation that is
  systematic (i.e., tending to one side or the
  other)
• Sampling error the inevitable result of trying
  to estimate parameters with a sample that is
  smaller than the entire population
• m.o.e. an estimate of sampling error (m.o.e.
  shrinks as sample size grows, assuming you have a
  random sample)
• Note Bias is avoidable. Sampling error is not.

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Fun Chart Who wins thiselection? (5.8 million
votes cast)
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Fun Chart Who wins thiselection? (5.8 million
votes cast)
Statistics Because of errors in the tabulation
process, the m.o.e. for each candidate is at
least several thousand votes, possibly as high as
60,000 votes. The initial tally shows Candidate A
with a lead of 537 votes over candidate B.
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Who do you think won?

• Candidate A, by 537 votes (no recount)
• Candidate A, maintaining a lead even after the
  recount
• Candidate B, pulling ahead after the recount
• Tie

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Tonights Theme(Try to guess it from these
examples.)

• Space aliens stare at Earth through powerful
  telescopes. They observe that most of the people
  buying diet soda are a bit overweight, to put it
  mildly. Conclusion Diet soda makes people fat.
• A teacher enforces discipline in the classroom by
  deducting one point for each minor infraction
  (burping, tardiness, etc.) and tells a student
  who has lost several points, Your actions have
  lowered your grade from A minus to B plus.
• Terrorists hijack airplanes and crash them into
  buildings, killing several thousand Americans.
  Spokesmen for the terrorists, as well as a number
  of international commentators, say that U.S.
  government policies are to blame.
• A Roman army unit performs poorly in battle, with
  several of the men deserting in fear. After the
  battle, the commander decimates the troops (i.e.,
  kills every tenth man present). The troops learn
  that if they desert, they will be sealing a death
  warrant for their friends still in the unit.
• A village under Nazi occupation revolts. In
  reprisal, the Nazis murder nearly all the
  villagers, but they also lay waste to several
  neighboring villages. The revolts quickly cease.
• A sheriff running for re-election proudly states,
  During my four years in office, the violent
  crime rate has dropped by 28. Vote for me to
  continue the progress!

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What is the theme?

• Space aliens are not very bright
• Correlation does not imply causation
• Distortion of cause and effect
• How to lie with statistics

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Cause and Effect

• A most interesting subject Even babies are
  fascinated by it!
• All public policy decisions hinge on cause and
  effect
• Warning Remember the Law of Unintended
  Consequences (examples of refrigerator
  subsidies, Australian rabbit invasion, AFDC)
• Difficulties
• Mathematics has nothing to say on the subject.
• We must turn to the relatively new science of
  statistics.
• There is only one way to prove cause and effect,
  and the conditions are rarely met.
• But . . . that does not stop politicians,
  journalists, and activists from asserting
  cause-and-effect relationships.

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Making it RealIran Group

• What economic statistics or intelligence
  statistics can be cited to show whether Iran is
  violating the NPT?
• What can we infer about Irans timetable for
  acquiring a nuclear capability? What
  extrapolation, subject to what set(s) of
  assumptions, can be made upon these statistics?
• What is the strategic effect upon Iran of the
  threat of massive nuclear retaliation? What
  quantitative evidence can we use, or is any
  evaluation simply a gut feeling?
• Can economic sanctions or military strikes cause
  changes in Iranian policies? Which would be more
  effective and under what circumstances?
• What would be the macroeconomic effects on the
  Iranian economy, other regional economies, and
  world commodities markets if Iranian oil supplies
  were disrupted?
• What is U.S. public opinion toward putting
  economic and/or military pressure on Iran, and
  how is public opinion likely to shift over time?
• Baseline statistics Daily oil consumption of the
  U.S., key allies, China, India, and the world
  daily oil production of Iran
• Oil reserve estimates based on petroleum
  engineers statistics

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Making it RealIran Group

• Bottom line for this group Your analysis will
  probably be qualitative, not quantitative.
• Geopolitical interactions are grounded in
  economic and statistical realities, but
  predicting how things will play out is
  extraordinarily difficult. (Chaos theory?)
• Diplomacy, nuance, gamesmanship, alliances,
  politics, and p.r. are more important factors.
• Mathematicians are of little value in this realm.
• Statisticians may be able to help with polling
  and econometric modeling.

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Making it RealEnergy Group

• The science of statistics is probably more useful
  for you than for the Iran group
• Does CO2 cause global warming?
• Do other greenhouse gases cause global warming?
• What fraction of global warming is caused by
  human activities (e.g., burning of fossil fuels)?
• Will changing our behaviors cause a reduction or
  reversal of global warming?
• What government policies on current and
  alternative fuels will cause changes in peoples
  behavior?
• To what degree do U.S. energy policies cause
  changes in other countries economies or
  behaviors?
• A high reliance on oil revenues in a country
  appears to be correlated with a low level of
  democracy and personal freedom. Is this
  correlation evidence of a cause-and-effect
  relationship, or can the correlation be explained
  by lurking variables?

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Making it RealCause and Effect in the News

• Do mercury-based preservatives in childhood
  immunizations cause autism? Many parents whose
  children suddenly became autistic shortly after
  having an immunization are convinced that this is
  so.
• Did Vioxx cause heart attacks and strokes? If so,
  should Merck be required to pay damages to
  patients who suffered a heart attack or stroke
  after taking Vioxx?
• Does second-hand cigarette smoke cause lung
  cancer or other diseases? If so, should smoking
  be banned in all indoor locations?
• Do American high school classrooms cause boys to
  lag behind girls academically? If so, should
  curricula and teaching styles be revamped? What
  would be the effects of doing that?
• Do silicone implants cause lupus and other
  autoimmune disorders in women?
• Did Zicam cause people to lose their senses of
  taste and smell?
• Do cell phones cause automobile accidents?

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Some Common Fallacies

• Anecdotal data
• Emotional appeals or ad hominem attacks
• COI, appearance of COI, or accusations of COI
• Post hoc, ergo propter hoc (roughly translated
  after this, therefore caused by this)
• Similar Correlation confused with causation
• Extrapolation (i.e., assuming trends will
  continue)
• Overanalyzing time series of uncontrolled systems
  (e.g., trying to predict the stock market by
  using technical analysis)

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Are there any people who know what theyre doing?

• Yes, a few.
• Everyone should take a course in statistics.
• A statistics course is one of the few courses
  where you are unlikely to study any actual
  statistics! (You will study the science and
  practice of statistics.) Actual statistics are
  seen in nearly all other courses history,
  biology, sociology, etc.

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Of the 1300 randomly chosen adult American
voters who were polled, 38 were satisfied with
President George W. Bushs performance in office.
The margin of error is plus or minus 3.

• I know exactly what the statement means.
• I know quite well what the statement means.
• I do not know what the statement means.
• I do not even know whether or not I know what the
  statement means.

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Of the 1300 randomly chosen adult American
voters who were polled, 38 were satisfied with
President George W. Bushs performance in office.
The margin of error is plus or minus 3.Exactly
what does this statement mean?

• The true parameter is between 35 and 41.
• The true statistic is between 35 and 41.
• The true parameter is probably between 35 and
  41.
• The true statistic is probably between 35 and
  41.

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On the previous slide, why did the correct answer
involve the word probably?

• sampling error
• bias
• lack of randomness in the sample
• sample size was too small for a believable survey
  of the entire nation

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If you are making public policy decisions, why
should you take nearly all news reporting (as
opposed to news analysis or commentary) with a
grain of salt?

• sampling error
• the most accurate reporting is usually internal
  to the government, not coming from the news media
• media bias
• anecdotal data

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How to Talk Back to a StatisticSource Darrell
Huffs classic 1950s book, How to Lie With
Statistics

• Who says so? (Beware of COI.)
• How does he or she know? (What methods were used
  to compute the statistic? Many numbers are simply
  unknowable in a practical sense.)
• Whats missing? (Ask what the m.o.e. is, what
  assumptions were used, what time period was used,
  and whether there was a control group.)
• Did someone change the subject? (Beware of
  semiattached data, gee-whiz graphs, and
  extrapolation.)
• Does it make sense? Modern-day buzzterm FACE
  VALIDITY.

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Regarding Face Validity . . .

• Use your common sense and read critically. Even
  reputable sources contain errors.
• Compute ratios or per capita values. (For any
  national budget number, simply take the number of
  billions and multiply by 3 or 4. Example A 50
  billion program is costing each adult in the
  country about 200.)
• Excerpt from The Washington Post Magazine on
  April 2, 2006 (posted on their website)Adult
  education is thriving nationwide, with more than
  92 million adults taking college classes. At the
  nearly 70 two- and four-year colleges in the
  Washington area, an estimated 175,000 adults are
  enrolled, 40 percent of them on a part-time
  basis.
• Which statistic in this excerpt lacks face
  validity?

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What is a statistic?

• a number that describes a population
• a fact
• a number computed from data
• a person who is the victim of crime or an accident

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What is a parameter?

• a number that describes a population
• a fact
• a number computed from data
• an adjustable constant, or a boundary condition
  for a problem

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What is the only way to establish cause and
effect?

• a careful observational study
• a careful observational study with a sufficiently
  large sample size and freedom from bias
• an experiment
• a controlled experiment

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On a scale of 1 to 7, please rate how you feel
about this statement I am planning to take a
statistics course sometime within the next three
years. (Mark 7 if you have already taken a
statistics course in high school, e.g., AP
Statistics.)

• Strongly Disagree
• Disagree
• Somewhat Disagree
• Neutral
• Somewhat Agree
• Agree
• Strongly Agree

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Q and A

• Thank you for your time and attention!
• Michael Hansen(e-mail modd at sign modd.net)
• St. Albans School of Public Service
• Washington, DC
• June 29, 2006