4'3 Relationships Between Categorical Variables

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4.3 Relationships Between Categorical Variables
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Categorical Variables

• When analyzing categorical variables we use
  counts or percents.
• Two-Way Table describes two categorical
  variables.

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Marginal Distributions

• Each marginal distribution from a two-way table
  is a distribution for a single categorical
  variable.
• Marginal distributions appear at the bottom and
  right margins.
• Gender and Age are marginal distributions
  below.

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Marginal Distributions

• Percents are often more informative than counts
  especially when making comparisons.

The percent of students who are 18 to 24 years
old
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Describing Relationships

• Conditional Distribution calculating the
  distribution of percents for one variable across
  some condition on the other variable.
• Different from Marginal which goes on in the
  margins, or counts for each row and column.

Ex) The conditional distribution of gender, given
that a student is 18 to 24 years old
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Conditional Distributions

• May be displayed using bar graphs

• Summary
• No single graph (such as a scatterplot) portrays
  the form of the relationship between categorical
  variables.
• No single numerical measure (such as the
  correlation) summarizes the strength of the
  association.

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Simpsons Paradox may be LURKING!
Ex) Do helicopters save lives? What is safer
helicopter evacuation or usual transport?

32 of helicopter patients died 24 of usual
transport died
Lets take a closer look
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Simpsons Paradox may be LURKING!

Both groups of victims have a higher survival
rate when evacuated by helicopter. The
seriousness of the accident was the lurking
variable (it is also categorical).
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Simpsons Paradox

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With Time Simpsons Paradox Challenge
Home Depot and Lowes are vying for Durhams Best
Local Employer award, to be given to the company
most committed to hiring local residents. While
both employers hired 300 new people in the past
year, Home Depot boasts that it deserves the
award because 70 of its new jobs went to local
residents, compared to only 60 for Lowes. Lowes
concedes that those percentages are correct, but
points out most of its new jobs were full-time,
while most of Home Depots were part-time. Not
only that, says Lowes, a higher percentage of its
full-time jobs went to local residents than did
Home Depots, and the same was true for part-time
jobs. Thus, Lowes argues, its a better local
employer than Home Depot. How is this possible?
Answers will vary.