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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

Measures of AssociationJune 25, 2008

Ivan Katchanovski, Ph.D.

POL 242Y-Y

measures of association
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
proportionate reduction of error pre
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
pre based measures of association
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
cramer s v chi square based measure of association
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
criteria of strength of association
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
direction of association
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
example
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)
example1
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?
spss commands
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