Contingency Tables and Related Data Analysis

CONTINGENCY TABLES

• Definition: A contingency table summarizes the relationship between two categorical variables. It can be referred to as a cross tabulation.

• Types:

  • Two-way: Involves two variables.

  • Three-way: Involves three variables.

  • Example: A 2 X 3 table represents a 2 category variable by a 3 category variable.

VARIABLES EXAMPLE

• Independent Variable: Age Group

• Dependent Variable: Preferred Immigration Policy

• Survey Data: World Values Survey, Australian Respondents 2018 includes preferences for immigration policy among age groups:

  • Up to 29 years: 178 respondents

  • 30-49 years: 510 respondents

  • 50 plus years: 1093 respondents

  • Total: 1781 respondents

PERCENTAGE ANALYSIS

• Purpose: Compare different group sizes using percentages to draw meaningful conclusions:

  • Up to 29 years:

  • Let anyone come: 11.24%

  • People come if jobs available: 50.56%

  • Strict limits: 37.08%

  • Prohibit: 1.12%

  • 50 plus years:

  • Let anyone come: 2.10%

• Comparison: Higher percentage of younger respondents prefer liberal immigration policy compared to older groups.

ADDITIONAL EXAMPLE

• Independent Variable: Immigrant Status

• Dependent Variable: Confidence in Courts

• Survey Data: World Values Survey, Australian Respondents 2018:

  • Confidence levels categorized by immigrant status.

SUMMARY OF FINDINGS

• Understanding Group Differences:

  • Use percentages to identify potential differences.

  • Consider calculation methodology: row vs column percentages.