Cross-Tabulation Analysis; Making Comparisons; Controlled Comparisons June 2, 2008 Ivan Katchanovski, Ph.D.

POL 242Y-Y

Cross-Tabulation

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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 2

Example: Cross-tabulation

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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 3

Example: Cross-tabulation Table 1. Preference for freedom and equality in the US and Canada, percent Freedom Equality Total, % N United States 67 33 100 1455 Source: 1996 Lipset/Meltz survey Canada 56 44 100 1702 4

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.

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Graphical Illustration 30 20 10 0 80 70 60 50 40 67 33 56 44 United States Freedom Canada Equality Figure 1. Preference for freedom and equality in the US and Canada, percent Source: 1996 Lipset/Meltz survey 6

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 7

Example: Additive Relationship

Table 2. Preference for freedom and equality in the US and Canada controlling for gender, % (fictional data) Freedom Equality Total, % US 75 25 100 Male Canada 63 37 100 US 59 41 100 Female Canada 48 52 100 8

Additive Relationship: Line Graph

60 50 40 30 20 10 0 41 25 52 37 Male Female US Canada Figure 2. Preference for equality in the US and Canada controlling for gender, % (fictional data) 9

Example: Spurious Relationship Table 3. Preference for freedom and equality in the US and Canada controlling for religiosity, % (fictional data) Freedom Equality Total, % US Religious Canada 75 25 100 74 26 100 Non-religious US Canada 52 48 100 50 50 100 10

Spurious Relationship: Line Grap

h

60 50 40 30 20 10 0 48 25 50 26 Religious Non religious US Canada Figure 3. Preference for equality in the US and Canada controlling for religiosity, % (fictional data) 11

Example: Interactive Relationship

Table 4. Preference for freedom and equality in the US and Canada controlling for race, % (fictional data) White Racial minorities US Canada US Canada Freedom Equality Total, % 75 25 100 60 40 100 60 40 100 58 42 100 12

Interactive Relationship: Line Graph 50 40 30 40 42 40 White 20 10 25 Racial minority 0 US Canada Figure 4. Preference for equality in the US and Canada controlling for race, % (fictional data) 13

Exercise Political party preference, 2006 Canadian Election Study Survey, % English French Liberal Conservative NDP Bloc Quebecois Other None/Don’t know Total, % N speaking 17 15 8 0 3 58 100 873 speaking 14 8 2 17 2 57 100 243 14