PS371003: Lecture 8

1
PS371-003 Lecture 8

• Measures of Association

2
Contingency Tables

• Contingency tables Crosstabs they display the
  relationship between categorical variables.
• They are called contingency tables because they
  allow us to examine a hypothesis that the values
  of one variable are contingent (dependent) upon
  those of another. Are most useful when measures
  of significance and association are included

3
Relationships Association

• Association measures the strength of a
  relationship
• Perfect
• A change in the independent variable is ALWAYS
  associated with a change in the dependent
  variable. Usually on a scale from 0 to 1
  where 1 equals a perfect relationship.
• Null
• A change in the independent variable is NEVER
  associated with a change in the dependent
  variable. A value of 0 equals a null
  relationship.

4
Measures of Association

• Nominal Association
• Chi-Square based measures
• Phi, Cramers V (symmetric)
• Phi is appropriate for 2 x 2 tables b/c it can be
  interpreted the same way that a correlation
  coefficient is interpreted (that X percent of the
  variance in the dependent variable can be
  explained by the independent variable). Larger
  tables can not be interpreted the same way b/c
  the value of Phi does not range between 0 1.
• Cramers V is the most used measure of
  association for Nominal data. It can be used for
  all size tables and is identical to Phi on 2 x 2
  tables. It ranges between 0 1 and thus is more
  similar to the correlation coefficient than Phi.
• Proportionate Reduction in Error (PRE) measures
• Lambda (asymmetric)
• you reduce the probability of incorrectly
  classifying the value of the dependent variable
  by knowing the value of an independent variable

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Measures of Association

• For Nominal by Interval association use the
  Correlation Ratio (ETA)
• E.g. difference of income by gender
• Ordinal Association
• Kendall's tau-b (smaller, generally 2x2 tables,
  square) symmetric
• Kendalls tau-c (for larger tables or not
  square) symmetric
• Gamma symmetric
• Somers d asymmetric

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Final Thoughts

• Significance and Association.
• Measures of significance are inferential and test
  the null hypothesis that the strength of an
  observed relationship is not different from what
  would be expected due to the chance of random
  sampling. Measures of association reflect the
  actual strength of the relationship. The two
  measures are both important and should be
  reported together when discussing findings.