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Cross-tabulation
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Cross-Tabulation Analysis; Making Comparisons; Controlled Comparisons
June 2, 2008
Ivan Katchanovski, Ph.D.
POL 242Y-Y
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Cross-Tabulation• Cross-tabulation: A method of hypotheses
testing– Very common– Very simple– Bivariate analysis– Appropriate for nominal, ordinal, and interval-
ratio variables
• Bivariate table of percentages– The dependent variable is in rows– The independent variable is in columns– Percentage totals are column totals
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Example: Cross-tabulation• Research hypothesis: Canadians are
more supportive of equality than Americans are
• The dependent variable: Preference for equality– in rows
• The independent variable: Country– in columns
Example: Cross-tabulation
Table 1. Preference for freedom and equality in the US and Canada, percent
Source: 1996 Lipset/Meltz survey
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United States Canada
Freedom 67 56
Equality 33 44
Total, % 100 100
N 1455 1702
Example: Cross-tabulation
• Comparison: – compare percentages across columns at the same value of
the dependent variable
– Look for significant differences: • A rule of thumb for survey data: 4% or more in expected
direction
• Example from Table 1: – 44% of Canadians, compared to 33% of Americans,
prefer equality over freedom
• Interpretation of results: – The cross-tabulation analysis supports the research
hypothesis.5
Graphical Illustration
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Figure 1. Preference for freedom and equality in the US and Canada, percent
Source: 1996 Lipset/Meltz survey
Controlled Comparisons• Analysis of the relationship between and independent
variable and a dependent variable controlling for another variable
• Types of relationships– Additive: Control variable adds to explanation of an
dependent variable by an independent variable
– Spurious: Relationship between an independent variable and a dependent variable disappears when a control variable is introduced
– Interactive: Relationship between an independent variable and a dependent variable depends on the value of control variable
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Example: Additive Relationship
Table 2. Preference for freedom and equality in the US and Canada controlling for gender, % (fictional data)
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Male Female
US Canada US Canada
Freedom 75 63 59 48
Equality 25 37 41 52
Total, % 100 100 100 100
Additive Relationship: Line Graph
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Figure 2. Preference for equality in the US and Canada controlling for gender, % (fictional data)
Example: Spurious Relationship
Table 3. Preference for freedom and equality in the US and Canada controlling for religiosity, % (fictional data)
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Religious Non-religious
US Canada US Canada
Freedom 75 74 52 50
Equality 25 26 48 50
Total, % 100 100 100 100
Spurious Relationship: Line Graph
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Figure 3. Preference for equality in the US and Canada controlling for religiosity, % (fictional data)
Example: Interactive Relationship
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White Racial minorities
US Canada US Canada
Freedom 75 60 60 58
Equality 25 40 40 42
Total, % 100 100 100 100
Table 4. Preference for freedom and equality in the US and Canada controlling for race, % (fictional data)
Interactive Relationship: Line Graph
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Figure 4. Preference for equality in the US and Canada controlling for race, % (fictional data)
Exercise
English-speaking
French-speaking
Liberal 17 14Conservative 15 8NDP 8 2Bloc Quebecois 0 17Other 3 2None/Don’t know
58 57
Total, % 100 100N 873 243 14
Political party preference, 2006 Canadian Election Study Survey, %