Chapter 5E SBM Statistical Reasoning

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Chapter 5E SBMStatistical Reasoning

• Correlation and Causality

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Seeking Correlation

• A correlation exists between two variables when
  higher values of one variable consistently go
  with higher values of another or when higher
  values of one variable consistently go with lower
  values of another.
• Ex. There is a correlation between the height
  and weight of people, the taller tend to weigh
  more than the shorter people.

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Types of Correlation

• Positive Correlation where both variables tend
  to increase (or decrease) together.
• Negative Correlation where the two variables
  tend to change in opposite directions, with one
  increasing while the other decreases.

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More Types of Correlation

• No Correlation where there is no apparent
  relationship between the two variables.
• Strength of Correlation where the more closely
  two variables follow the general trend, the
  stronger the correlation (which may be either
  positive or negative).
• A Perfect Correlation is where all data points
  lie on a straight line.

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A Scatter Diagram

• A Scatter Diagram may be used to represent the
  values of two variables.
• The diagram to the right compares a persons
  height to their GPA.
• Does in Correlate?
• Yes and its positive

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Establishing Causality

• Please copy the chart for
• Guidelines for Establishing Causality
• On page 348
• You have 5 minutes.
• Then, make sure you understand what you just put
  down on paper!!!

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Levels of Confidence?

• When you have discovered a correlation, but
  cannot determine whether it implies causality.
  You have a possible cause.
• In the legal system, possible cause (such as
  thinking that a particular suspect caused a
  particular crime) is often the reason for
  starting an investigation.

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2nd Level of Confidence?

• If you have good reason to suspect that the
  correlation involves cause, perhaps because some
  of the guidelines for establishing causality are
  satisfied, you have probable cause.
• In the legal system, probable cause is the
  general standard for getting a judge to grant a
  warrant for a search or a wiretap.

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3rd Level of Confidence?

• If you have found a physical model that is so
  successful in explaining how one thing causes
  another that it seems unreasonable to doubt the
  causality, then you have cause beyond a
  reasonable doubt.
• In the legal system, cause beyond a reasonable
  doubt is the usual standard for a conviction and
  generally demands that the prosecution has shown
  how and why the suspect committed the crime.

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Example One

• Would you expect a positive correlation, a
  negative correlation, or no correlation between
  the variables distance traveled in a car and
  gallons of gasoline used?
• ANS
• Positive correlation The greater the distance
  traveled the more gasoline will be consumed, so
  higher values of the first variable will go with
  higher values of the second.
• See next slide!

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Check to see Correlation?
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Example Two

• Would you expect a positive correlation, a
  negative correlation, or no correlation between
  the variables a student's height and his score on
  the SAT?
• ANS
• No correlation there is no reason to suspect
  that taller people will either consistently score
  higher or consistently score lower than shorter
  people on the SAT.
• See next slide!

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Check to see Correlation?
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Example Three

• Do you think that the following correlation is an
  example of coincidence, a common cause, or
  causality? When I flip the switch, the light
  comes on.
• ANS
• Causality

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Example Four

• Do you think that the following correlation is an
  example of coincidence, a common cause, or
  causality? Whenever I wash my car, it rains.
• ANS
• Coincidence

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Homework

• 5E s 2 - 5, 9, 10, 16 21
• Chapter 5A 5E Test next block.
• You may use a 3 x 5 card only