Help

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Help!

• Final non-cumulative (50 questions)
• Optional extra credit exam (50 points)
• Exam will be last day of class for those who want
  it, otherwise as scheduled

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Statistics and Risk
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Objectives

• Not to teach you how to calculate risk
• Thats what statistics courses are for
• Understand what people mean by probability and
  risk
• Be able to identify common fallacies and
  deceptions

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Measurement

• Apart from counting whole numbers, nothing can
  ever be measured exactly
• Fuzziness of phenomenon
• Instrument errors
• Observer bias
• Best we can do is describe range of values
• Earth-Sun Distance 149,597,870.66 .05 km

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Statistical Terms

• Probability Likelihood of an event happening
• Scatter How much the data deviate from an ideal
  pattern
• Error Bounds () Range of values where some
  measurement is most likely to fall
• Correlation How well two sets of data relate to
  each other

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Probability

• Number of ways something can happen
• Number of ways everything can happen
• Rolling a 5 with a die 6 ways die can land, one
  of them is a five, so probability 1/6
• Probability of one head in 5 tosses 2x2x2x2x2
  possible sequences, 5 ways to get one head, so
  probability 5/32

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Sometimes Its Easier to Calculate the Chances
Something Wont Happen

• How many people do you have to get in a group
  before theres a 50-50 chance two will share a
  birthday?
• Two people chances of not sharing are 364/365
• Third person 363/365, fourth 362/365, etc.
• Keep multiplying until odds drop below 50
• Need only 28 people

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Real World Probability

• Far too complex to calculate directly
• Estimate from observations of events
• Number of events/Possible Occurrences
• 40,000 auto fatalities/year ? 280,000,000
  Americans 1/7000

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Real World Probability

• 50 chance of rain
• When we had similar weather in the past, it
  rained 50 of the time
• If we make a large number of observations under
  similar weather conditions, we expect it to rain
  50 of the time
• 50 of the viewers in our area will see rain

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Errors and Confidence

• Errors tend to follow predictable patterns

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Example

• Current velocity, km/hour
• Data Values 9.6, 9.8, 10, 9.9, 10.1, 9.8, 9.9,
  9.7, 10, 10.2
• Average 9.9
• Standard Deviation 0.18
• 68 chance real value is between 9.72 and 10.08
• 95 chance its between 9.54 and 10.26

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Blowing Up The World

• Manhattan Project, 1945
• What are the odds that an atomic explosion would
  trigger nuclear fusion in the atmosphere?
• All the data suggested it was impossible, but
  wed really like to be sure
• Settled on odds of 1 in 3 million (How did they
  get that number?)

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Blowing Up The World

• So any nuclear blast has a 1 in 3 million chance
  of blowing up the world?
• No. Manhattan Project Scientists Knew
• Measured properties of nuclear reactions
• What would be necessary for fusion to occur?
• Real Question What were the odds the
  measurements were so far off that fusion would
  occur despite best data?

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Blowing Up The World
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Correlation

• Correlation is not causation
• Does A cause B?
• Does B cause A?
• Are both related to something else?
• Correlation is never perfect in the real world

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SAT and Income

• Students from higher-income homes tend to get
  higher SAT scores
• SAT reflects social class more than academic
  potential (Ralph Nader)
• Or, do people with more intelligence earn more
  and pass intelligence and behavior on to
  offspring?

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Correlation is Never Perfect

• A high proportion of child abusers were abuse
  victims themselves
• Why dont all abuse victims become abusers?
• Why do some non-victims become abusers?

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Statistical Significance

• Statistically Significant
• Difference between Measurements whose scatter
  doesnt overlap
• Data sets with very strong correlation
• Not Statistically Significant
• Difference between Measurements whose scatter
  overlaps
• Data sets with weak correlation

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Example The Bell Curve
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Two Common Types of Bad Data

• Gee Whiz" Facts
• Anecdotal Evidence

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"Gee Whiz" Facts

• A Million Children Are Reported Missing Every
  Year
• There are about 50 million people in the U.S.
  under 18.
• Taken literally, 1/3 of all children disappear
  before adulthood. I think we'd notice that.
• The vast majority of missing children are found
  within a few hours.
• At any given time the FBI has less than 100
  stranger abductions on file.

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"Gee Whiz" Facts

• Suicide Is the ---th Leading Cause of Death
  among Teen-agers
• Now think about it. What can kill teen-agers?
• They're beyond the age of childhood diseases
  (most of which are under control)
• Too young for diseases of old age
• That leaves accident, homicide and suicide

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Anecdotal Evidence

• Anecdotal Evidence is evidence based on single
  noteworthy events or observations
• To Be Valid, Anecdotal Evidence
• Must Be True
• Must Be Representative

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Anecdotal Evidence and Urban Legends

• Favorite themes
• Horror
• Violation of Taboo
• Plausible
• Have Local Details Added in Retelling
• Can Never Trace to Original Source

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Some Urban Legends

• Alligators in New York sewers
• Foreign objects in Halloween candy
• Headlight flash gang initiation
• Proctor and Gamble Logo
• FCC to ban religious broadcasting
• Most e-mail virus alerts

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An Environmental Urban Legend

• Nests of baby rattlesnakes have killed small
  children who played in outdoor play areas at fast
  food restaurants
• Plausible, not impossible
• But hasnt happened
• Bogus pro-environmental legends wreck credibility
  of environmentalism
• Anti-environmental legends create false
  impressions of facts

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Anecdotal Evidence

• To Be Valid, Anecdotal Evidence
• Must Be Representative
• Example The millionaire who pays no income tax

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The Reality Looks Like This

• (Source, 2000 IRS data 2003 Statistical Abstract
  of US Table 491)

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Clustering

• Airplane crashes (disasters, deaths) come in
  Threes
• For example, in 1997
• Gianni Versace (July 15, 1997)
• Princess Diana (August 31, 1997)
• Mother Theresa (September 5, 1997)
• John Denver (October 12, 1997)
• Ben Hogan, Eugene Schumacher, James Stewart,
  William S. Burroughs?
• A rare event does not make a recurrence more or
  less likely

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Clustering

• 7 holes in one on 16th hole of Masters in 68
  years
• 7/(68 years x 4 rounds x 100 players) 1
  in 4000
• In 2004, Padraig Harrington made a hole in one.
• What are the odds that the very next player, Kirk
  Triplett, also would?
• Answer 1 in 4000

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After The Fact Statistics

• Chances of two successive holes in one on 16th
  hole at Masters 1 in 4000 x 4000 16,000,000
• With 4 rounds, 100 players in field each year,
  would happen once every 40,000 years
• Therefore, didnt happen

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After The Fact Statistics

• This room holds about 100 people
• 100,000 people in Green Bay
• Chance of a randomly selected person being here
  at any given time 1/1000
• Chance of any 50 given people being here at same
  time (1/1000)50 1 in 10150
• Therefore none of you are here

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After The Fact Statistics

• With almost infinite outcomes possible, any
  outcome is unlikely
• But some outcome will happen
• We single out the special events
• The cup is no more unlikely than any other point
  on the green for a ball to land, but we dont
  care about all the others

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Risk

• Perceived benefit people underestimate risk,
  overestimate likelihood of benefit
• Perceived harm people overestimate risk
• No such thing as zero risk

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11,000,000 Risks

• Smoking 1.4 cigarettes (cancer, heart disease)
• Two days in large city (air pollution)
• 10 miles by bicycle (accident)
• 1000 miles by jet (accident)
• One chest X-ray (cancer)
• 5 years on boundary of nuclear plant
• 100 charcoal broiled steaks (cancer)