CrossTabulation

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Cross-Tabulation

• 2007-02-14

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Social Science

• One of the main objectives is to make sense out
  of human and social experience by uncovering
  regular patterns among events
• Forest vs. Trees

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Cross-Tabulation

• A technique for analyzing the relationship
  between two or more variables
• How the variables are associated
• Strength of the association
• Its direction (when appropriate)

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Constructing the Table

• The tables title is descriptive
• Dependent/Independent are the row/col variables
• Layout is clear and concise
• Marginals
• Overall N
• Cell percentages should sum to 100 for each
  level of the independent variable
• Source of data

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Properties of the Relationship

• Questions to ask when examining a bivariate
  relationship
• Does there appear to be an relationship?
• How strong is it?
• What is the direction of the relationship?

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Existence of the Relationship

• A relationship is said to exist between two
  variables if the percentage distributions vary
  across the different categories of the
  independent variable
• Eye-Ball Test

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Existence of the Relationship
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Strength of the Relationship

• The larger the percentage difference across the
  categories, the stronger the association
• Measures of association
• Tau-b, Tau-C, Gamma, Lamda

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Direction of the Relationship

• Ordinal or Interval data
• Positive relationship ? the variables vary in the
  same direction
• Negative relationship ? the variables vary in
  opposite directions

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Direction of the Relationship
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Elaboration

• Allows us toe test for nonspuriousness
• It cannot be explained away by other variables
• Clarifies the causal sequence of the bivariate
  relationship
• Intervening variables
• Specifies the different conditions under which
  the original relationship might hold

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Spurious Relationship
Property Damage
Firefighters
Firefighters
Size of Fire
Property Damage
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Spurious Relationships

• Divide the observations into subgroups on the
  basis of the control variable
• Reexamine the relationship between the original
  variables
• Compare the partial relationships with the
  original relationship
• In a spurious patter, the partial relationship
  will be much weaker the the original

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Intervening Variable

• A control variable that follows an independent
  variable but precedes the dependent variable in a
  causal sequence

Religion
Preferred Family Size
Support for Abortion
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Limitations of Elaboration

• How do we know which variables to control for?
• Importance of theory as a guide