CrossTabulation Analysis Making Comparisons Controlled Comparisons June 2

Cross-Tabulation Analysis; Making Comparisons; Controlled Comparisons June 2, 2008 Ivan Katchanovski, Ph. D. POL 242 Y-Y

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 2

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 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 Canada 56 44 100 1702 Source: 1996 Lipset/Meltz survey 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. 5

Graphical Illustration 80 70 60 50 40 30 20 10 0 67 56 44 33 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) Male Female US Canada Freedom 75 63 59 48 Equality 25 37 41 52 Total, % 100 100 8

Additive Relationship: Line Graph 60 50 40 30 20 10 0 52 41 37 25 US Male Female 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) Religious Non-religious US Canada Freedom 75 74 52 50 Equality 25 26 48 50 Total, % 100 100 10

Spurious Relationship: Line Graph 60 50 48 Religious 30 20 25 26 Nonreligious 10 0 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 Freedom 75 60 60 58 Equality 25 40 40 42 Total, % 100 100 12

Interactive Relationship: Line Graph 50 40 40 30 25 20 10 42 40 White 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, % Liberal Conservative NDP Bloc Quebecois Other None/Don’t know Total, % N Englishspeaking 17 15 8 0 3 58 100 873 Frenchspeaking 14 8 2 17 2 57 100 243 14