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**Association Between Two Variables Measured at the Nominal Level**

Chapter 13 Association Between Two Variables Measured at the Nominal Level

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**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.

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**Nominal Level Measures of Association**

For nominal level variables, there are two commonly used measures of association: Phi or Cramer’s V Lambda

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

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**Nominal Measures: Cramer’s V**

Cramer’s V is used for tables larger than 2x2. Formula for Cramer’s V:

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**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

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**Strength of Phi or Kramer’s V**

Value Strength Between 0.0 and 0.10 Weak Between 0.10 and 0.30 Moderate Greater than 0.30 Strong

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**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

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**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.

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**Nominal Measures: Lambda**

Formula for Lambda:

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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

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**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) = = 15 Lambda = (E1-E2)/E1 = (22-15)/22 = 7/22 = .32 Low Author. High Author. Totals Low Efficiency 10 12 22 High Efficiency 17 5 27 44

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**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%.

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**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.

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**Calculate lambda for this example.**

Low Author. High Author. Totals Low Efficiency 2 (7%) 8 (47%) 10(23%) High Efficiency 25 (93%) 9 (53%) 34(77%) 27(100%) 17(100%) 44(100%)

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