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Measures of Association June 25, 2008

Measures of Association June 25, 2008. Ivan Katchanovski , Ph.D. POL 242Y-Y. Measures of Association. Association refers to the relationship between two (or more) variables Example: Relationship between preference for freedom and national culture

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Measures of Association June 25, 2008

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  1. Measures of AssociationJune 25, 2008 Ivan Katchanovski, Ph.D. POL 242Y-Y

  2. Measures of Association • Association refers to the relationship between two (or more) variables • Example: Relationship between preference for freedom and national culture • Measures of Association provide information about: • Strength of relationship • Direction of association (ordinal or interval-ratio variables) • Helpful in tests of research hypotheses

  3. Proportionate Reduction of Error (PRE) • A logical model for assessing the strength of a relationship by asking how much knowing values on one variable would reduce our errors in guessing values on the other • Example: If we know how much education people have, we can improve our ability to estimate their income, thus indicating there is a relationship between the two variables

  4. PRE-Based Measures of Association • For nominal variables: If at least one variable is nominal • Lambda: based on ability to guess values on one of the variables • For ordinal variables: • Gamma: based on guessing the ordinal arrangement of values • Kendall’s tau-b • If the dependent and independent variables have the same number of categories • Kendall’s tau-c • If the dependent and independent variables do not have the same number of categories

  5. Cramer’s V: Chi-square Based Measure of Association • Non-PRE measure • Cramer’s V formula: _______________________________ • Cramer’s V= √χ2 /N(Minimum of rows-1 or columns-1) • Varies between 0 (no association) and 1 (perfect association) • Most appropriate for nominal variables

  6. Criteria of Strength of Association • Lambda and Cramer’s V • Vary between 0 (no association) and 1 (perfect association) • Gamma, Kendall’s tau-b, Kendall’s tau-c • Vary between -1 (perfect negative association) and 1 (perfect positive association) • 0: no association • 0-0.1: weak association • 0.1-0.3: moderate association • 0.3-1.0: strong association

  7. Direction of Association • Direction of the association (ordinal or interval-ratio variables): • Positive association: relationship where the variables vary in the same direction • Example: Positive association between income and education level • Negative association: relationship where the variables vary in opposite directions

  8. Example Table 1. Preference for freedom and equality in the US and Canada, percent Source: 1996 Lipset/Meltz survey • Nominal independent variable: Country • Cramer’s V= 0.108 (moderate association) • Lambda=0.092 (weak)

  9. Example Table 1. Confidence in television in Canada by education level, 2000 World Values Survey, % • Ordinal variables: Confidence in television and education • Gamma=0.183 (moderate level of association) • The dependent and independent variables do not have the same number of categories • Kendall’s tau-c=0.093 (weak level of association) • What is direction of association between these variables?

  10. SPSS Commands • SPSS Commands for Measures of Association: • Analyze=Descriptive Statistics-Crosstabs • “Row” box: select dependent variable • “Column” box: select independent variable • “Cells” Option: Column percentages • “Statistics” Option: Chi-square and measure of association • For nominal variables: Cramer’s V or Lambda • For ordinal variables: Gamma or Kendall’s tau

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