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Contingency Tables II

Learn about Gamma, Cramer’s V, and Lambda measures to assess association strength between variables. Explore how to set up contingency tables and calculate these measures effectively. Discover the predictability model for examining variable predictability.

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Contingency Tables II

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  1. Contingency Tables II

  2. Homework review • Chi square • Cramer’s V

  3. Measures of associationGamma () • Used with ordinal level data • Also if one of the variables is a nominal dichotomy • Assesses the strength of the association between variables • Ranges from - 1.0 to + 1.0 • 0 means no relationship • -1.0 and +1.0 indicate a perfect relationship

  4. Gamma () • Contingency table is set up with independent variable as column labels and dependent variable as row labels. • The values for each variable are placed in order (high to low or low to high). • The placement order must be consistent for both IV and DV. • We will work only with 2X2 tables.

  5. Gamma () • Gamma is calculated on a basis of paired observations • The cells where both the DV and IV are consistent (both high or both low) are called the concordant pair. • The cells where one variable is high and the other low are called the discordant pair.

  6. Gamma ()

  7. Gamma () • Overhead - example

  8. Measures of associationlambda () • Used where at least one variable is nominal and is not a dichotomy • asymmetric - unlike Cramer’s V and gamma, the value depends on which variable is the dependent variable • Ranges from 0 to +1

  9. lambda () • Other measures of association we have studied examine how 2 variables covary • Not possible for nominal level data • Instead, we use a predictability model • How well can we predict the category of the dependent variable if we know the independent variable? • The proportional reduction in error (PRE)

  10. lambda ()

  11. lambda () • Overhead - example

  12. General notesmeasures of association • Do not compare different measures of association. • You can’t assume that a relationship with a Cramer’s V = .15 is weaker than a relationship with a gamma = .45 • Calculating these measures of association for anything larger than a 2X 2 table is cumbersome • Let the computer do the work

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