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, %