Measures of Association June 25, 2008

1 / 10

# Measures of Association June 25, 2008 - PowerPoint PPT Presentation

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## Measures of Association June 25, 2008

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Measures of AssociationJune 25, 2008

Ivan Katchanovski, Ph.D.

POL 242Y-Y

Measures of Association
• Association refers to the relationship between two (or more) variables
• 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)
• 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
• 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
• 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
• 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 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

Source: 1996 Lipset/Meltz survey

• Nominal independent variable: Country
• Cramer’s V= 0.108 (moderate association)
• Lambda=0.092 (weak)
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 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