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

2. 2 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

3. 3 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

4. Example: Cross-tabulation Table 1. Preference for freedom and equality in the US and Canada, percent Source: 1996 Lipset/Meltz survey 4 United StatesCanada Freedom6756 Equality3344 Total, %100 N14551702

5. 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

6. Graphical Illustration 6 Figure 1. Preference for freedom and equality in the US and Canada, percent Source: 1996 Lipset/Meltz survey

7. 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

8. Example: Additive Relationship Table 2. Preference for freedom and equality in the US and Canada controlling for gender, % (fictional data) 8 MaleFemale USCanadaUSCanada Freedom75635948 Equality25374152 Total, %100

9. Additive Relationship: Line Graph 9 Figure 2. Preference for equality in the US and Canada controlling for gender, % (fictional data)

10. Example: Spurious Relationship Table 3. Preference for freedom and equality in the US and Canada controlling for religiosity, % (fictional data) 10 ReligiousNon-religious USCanadaUSCanada Freedom75745250 Equality25264850 Total, %100

11. Spurious Relationship: Line Grap h 11 Figure 3. Preference for equality in the US and Canada controlling for religiosity, % (fictional data)

12. Example: Interactive Relationship 12 WhiteRacial minorities USCanadaUSCanada Freedom7560 58 Equality2540 42 Total, %100 Table 4. Preference for freedom and equality in the US and Canada controlling for race, % (fictional data)

13. Interactive Relationship: Line Graph 13 Figure 4. Preference for equality in the US and Canada controlling for race, % (fictional data)

14. Exercise English- speaking French- speaking Liberal1714 Conservative158 NDP82 Bloc Quebecois017 Other32 None/Don’t know5857 Total, %100 N873243 14 Political party preference, 2006 Canadian Election Study Survey, %