Relationships in Categorical Data

1
Section 2.5

• Relationships in Categorical Data

2
Nutritional Status of Elementary School Children
vs. Their Academic Performance?

• Nutritional Status Categorized
• Poor, Adequate, or Excellent
• Academic Performance
• Below Avg., Avg., or Above Average
• Data Summarized in two Way Table

3
Marginal Distributions

• Row variable
• Column Variable
• Give the marginal distribution for each variable.

4
Conditional Distributions

• Explanatory Variable
• Response Variable
• Conditional Distributions(Condition on each value
  of the explanatory variable.)
• Of the 290 students with poor nutritional status,
  
• ____________have below avg. performance
• _____________ have avg. performance
• _____________ have above avg. performance

5
Conditional Distributions

• The three percentages found make up the
  conditional distribution of academic performance
  given poor nutritional status

6
Find and sketch the conditional distributions of
academic performance for students with other
nutritional statuses.
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Examining Relationship

• Compare the academic performance of students with
  each of the nutrition levels. Briefly describe
  the most important differences, and back up your
  description with percents.
• What is the advantage to using percentages
  instead of counts for heights of each rectangle?

8
Simpsons paradox

• The University of California at Berkeley was
  charged with having discriminated against women
  in their graduate admissions process from the
  fall quarter of 1973.

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Simpsons Paradox

• Fill in the following two-way table
• Of the men who applied, what percentage were
  admitted?
• Of the women who applied, what percentage were
  admitted?
• Does this support the claim that men were given
  preferential treatment in admissions
  considerations? Explain why or why not.

10
Simpsons Paradox

• What programs were responsible for the
  mistreatment of women?
• Does it seem as if any program is responsible for
  the mistreatment of women?
• Use data to explain the paradox.

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Simpsons paradox

• Simpons paradox The comparison reverses
  direction when made over all programs than when
  made for each program individually.

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Summary

• Marginal Distributions
• Conditional Distributions
• Look for relationship in bar graphs showing the
  conditional dist. Of the response for each level
  of the explanatory.
• Simpsons Rule What it is and how it happens.