AP STATISTICS LESSON 4

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AP STATISTICSLESSON 4 3 ( DAY 1 )

• RELATIONS IN CATAGORICAL DATA

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ESSENTIAL QUESTION What relationships do
categorical variables have?

• To analyze two way tables.
• To create marginal distributions.
• To explain the phenomena known as Simpsons
  Paradox.

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Analyzing Categorical Data

• To analyze categorical data we use counts or
  percents of individuals that fall into various
  categories.
• Two way tables contain two variables, one
  represented in the rows and one in the columns.

4
Definitions

• Marginal distributions The totals of each row
  and column that appear in the margins are
  referred to the marginal distributions.
• Roundoff error The difference between actual
  and the marginal distributions do to rounding of
  the sums.
• Conditional distribution The counts or percents
  of a given categorical variable.

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Simpsons Paradox

• Simpsons paradox refers to the reversal of
  the direction of a comparison or an association
  when data from several groups are combined to
  form a single group.

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Describing Relationships

• To describe relationships among categorical
  variables, calculate appropriate percents from
  the counts given. We use percents because counts
  are often hard to compare.
• A bar graph compares the sizes of different
  items. The horizontal axis of a bar graph need
  not have any measurement scale but simply
  identify the items being compared.