Chapter 3E SBM Numbers in the Real World

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Chapter 3E SBMNumbers in the Real World

• How Numbers Deceive
• Polygraphs, Mammograms, and more

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How numbers lie.

• The polygraph test is considered to be reliable.
  They are reputed to be 90 accurate.
• Therefore, only 10 of the people who fail the
  test are telling the truth. Or is it more?
• In this lesson, we will discuss several ways in
  which numbers can deceive.

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Example One

• A T.V. producer tested her theory that watching
  her new television program improves a childs
  reading ability.
• She designed a reading test and gave it to 500
  children.
• The following table summarizes the data.

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Example One (cont)

• What percentage of the 250 children who watch the
  program passed the test?
• 163 / 250 65.2
• What percentage of the 250 children who do not
  watch the program passed the test?
• 46 / 250 18.4

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Example One (cont)

• Does watching the program improve a childs
  reading ability?
• According the the survey yes.
• How are these numbers deceiving?
• Could the test be written to have (some)
  questions that could only be answered correct if
  you watched the program?
• Or maybe (some) concepts that reviewed in the
  program?

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Simpsons Paradox

• This example illustrates that it is possible for
  something to appear better in each of two group
  comparisons, but not actually better (or worse)
  overall.
• Is it possible that watching a T.V. program will
  help a childs reading ability? Yes, it is
  possible, but come on.
• Simpsons paradox arises often and is one way in
  which numbers can deceive
• Look at examples 1 - 5 on pages 191-197.

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Homework

• 3E 1, 2, 5, 10
• 3D 3E Quiz next block.
• Please show all work.