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Contingency Tables II

Contingency Tables II. Homework review. Chi square Cramer’s V. Measures of association Gamma ( ). 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

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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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