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Chapter 13

Chapter 13. Association Between Variables Measured at the Nominal Level. Chapter Outline. Introduction Chi Square-Based Measures of Association Proportional Reduction in Error (PRE). Chapter Outline. A PRE Measure for Nominal-Level Variables: Lambda The Computation of Lambda

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Chapter 13

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  1. Chapter 13 Association Between Variables Measured at the Nominal Level

  2. Chapter Outline • Introduction • Chi Square-Based Measures of Association • Proportional Reduction in Error (PRE)

  3. Chapter Outline • A PRE Measure for Nominal-Level Variables: Lambda • The Computation of Lambda • The Limitations of Lambda

  4. Nominal Level Measures of Association • It is always useful to compute column percentages for bivariate tables. • But, it is also useful to have a summary measure – a single number – to indicate the strength of the relationship.

  5. Nominal Level Measures of Association • For nominal level variables, there are two commonly used measures of association: • Phi or Cramer’s V • Lambda

  6. Nominal Measures: Phi • Phi is used for 2x2 tables. • The formula for Phi:

  7. Nominal Measures: Cramer’s V • Cramer’s V is used for tables larger than 2x2. • Formula for Cramer’s V:

  8. Nominal Measures: Phi • The phi for Problem 12.1 is 0.33. • This is a strong association.

  9. Limitations of Phi • Phi is used for 2x2 tables only. For larger tables, use V. • Phi (or V) is an index of the strength of the relationship only. It does not identify the pattern. • To analyze the pattern of the relationship, see the column %s in the bivariate table.

  10. Nominal Measures: Lambda • Like Phi, Lambda is used to measure the strength of the relationship between nominal variables in bivariate tables. • Unlike Phi, Lambda is a PRE measure and its value has a more direct interpretation. • While Phi is only an index of strength, the value of Lambda tells us the improvement in predicting Y while taking X into account.

  11. Association and Bivariate Tables • To compute λ, we must first find E1 and E2: • E1 = N – largest row total = 44 – 22 = 22 • E2 = For each column, subtract the largest cell frequency from the col. total = (27 – 17) + (17 – 12) = 10 + 5 = 15

  12. Nominal Measures: Lambda • Formula for Lambda:

  13. Nominal Measures: Lambda • Lambda is a PRE measure. • A Lambda of .32 means that authoritarianism (X) increases our ability to predict efficiency (Y) by 32%.

  14. The Limitations of Lambda • Lambda gives an indication of the strength of the relationship only. • It does not give information about pattern. • To analyze the pattern of the relationship, use the column %s in the bivariate table. • When row totals are very unequal, lambda can be zero even when there is an association between the variables.

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