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Chapter 13

Chapter 13 . Association Between Two Variables Measured at the Nominal Level. Nominal Level Measures of Association. It is always useful to compute column percentages for bivariate tables.

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Chapter 13

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

  2. 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. That’s what we’ll learn about in this chapter.

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

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

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

  6. SPSS: Phi and Kramer’s V • SPSS has both instructions combined into one • You need to know which one applies • Phi if it’s a 2 x 2 table • Kramer’s V for any other cross tabulation

  7. Strength of Phi or Kramer’s V

  8. Let’s ask SPSS to calculate a few chi square based measures • Class and happiness • Ager3 and grass • Ager3 and attend • Attend and grass • Attend and happy

  9. Nominal Measures: Lambda • Like Phi and Kramer’s V, Lambda is used to measure the strength of the relationship between nominal variables in bivariate tables. • Unlike Phi, Lambda is a PRE(proportional reduction of error) 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.

  10. Nominal Measures: Lambda • Formula for Lambda:

  11. Lambda as PRE measure • E1 = errors made in predicting the dependent variable without knowing the independent variable = N – largest row total • E2 = For each column, subtract the largest cell frequency from the col. total and add those values • This will become more clear when we look at an example

  12. 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 Lambda = (E1-E2)/E1 = (22-15)/22 = 7/22 = .32

  13. Nominal Measures: Lambda • Lambda is a PRE measure. • A Lambda of .32 means that knowing 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 the mode is the same in each column of the independent variable, lambda will be zero even if a relationship exists. Thus we request both lambda and Kramer’s V/Phi.

  15. Calculate lambda for this example.

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