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

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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 ValueStrength Between 0.0 and 0.10 Weak Between 0.10 and 0.30 Moderate Greater than 0.30 Strong

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 E 1 and E 2 : E 1 = N – largest row total = 44 – 22 = 22 E 2 = 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 High Efficiency17522 Totals271744

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. Low Author. High Author. Totals Low Efficiency2 (7%)8 (47%)10(23%) High Efficiency25 (93%)9 (53%)34(77%) Totals27(100%)17(100%)44(100%)


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