Scientific Inquiry SCI 105'020

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Scientific Inquiry SCI 105.020

• Statistical Models and Probability

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Recap Ex 2.7

• Analyze the findings reported in the May 8, 1987
  issue of Science
• Identify the four components involved in Model
  Evaluation process
• Run the six-step program described in the text to
  summarize what you see from the report

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The Four Components
Real World Dinosaurs extinct 65m-yr ago What
caused it?
Model Single catastrophic Eventextraterrestrial
body hittingcaused it
Fit
Observation
Reasoning
Calculation
Prediction Cracks in quartz Debris blocking
sunlight for months or years ? Climate cooled
down ? Death of habitants on earth
Agree
Data Unique crack patterns in quartz particles
Unusually high concentration of iridium found
all over the world
Size and speed fit or not?
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The Evaluation Process

• RW extinction of dinosaurs What caused it?
• Model two alternative theories
• Single catastrophic event ? hit by an
  extraterrestrial body
• A series of volcanic eruptions
• (New) Data found all over the world
• Unique crack patterns in quartz particles, and
• Unusually high concentration of iridium
• Prediction
• same as what the new data shown
• Size and speed prediction seemed reasonable
• Data-prediction agreement GOOD ? Model fit RW

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Why Statistical/Probabilistic Models?

• Widely used in science
• Social/behavioral sciences
• Public polls and surveys
• Testing theories like sunlight helps prevent
  depression
• Bio-medical sciences
• Can also be used in daily life
• Professional sports
• AFC vs. NFC which conference has stronger teams?
• NBA is the belief in hot hand supported by
  historical data?

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Modeling with Statistical Hypothesis

• Statistical hypothesis seem to be the only
  rational way to answer certain questions
• What percentage of American women between the
  ages of 20 to 30 hold a full-time job?
• Exceedingly difficult
• Very costly
• Its impractical or even impossible to seek for
  characteristics in large populations
• Instead, we can proximate them using small samples

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Casual Models Casual Hypothesis

• Behavioral/bio-medical scientists concern about
  causes of characteristics exhibited by
  individuals
• Does the dietary intake of cholesterol cause
  heart attacks in men?
• Cause or Correlation?

input
output
blackbox
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The Elements of a Statistical Study

• Terms associated with RW phenomenon
• Population the object of the investigation
• A property is a characteristic that may exhibit
  in the population
• Also known as a variable in the sense that it can
  be measured or classified to describe the
  property
• Also known as a parameter as defined in the
  handout
• Terms associated with model
• Sample selected members of the population
• Statistics a number computed from data that
  describes a characteristic of a sample

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Stats as Predictions to Parameters

• Theme
• A statistic is computed from a sample to
  predict the parameter for the whole population.
• Ex 1 average height of a Mercer Student

Population Havg XXX
Population size 8000
Sample havg xxx
Sample size 200
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Descriptive Statistics

• A graphical display of data
• Histograms
• Numerical summaries of data
• Center
• Spread
• Shape
• Outlier
• (See handout and sample
• worksheet for details)

Super Bowl Scores (1967-2001)
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Announcements

• H/W Assignment 2
• Ex 7 p 8 in the handout
• Create a histogram
• Draw a boxplot and more as specified
• Read the sections 5.3 through 5.7 (pp 124-137) in
  Gieres text