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 The Limitations of Lambda

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.

Nominal Level Measures of Association

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

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

Nominal Measures: Cramer’s V Cramer’s V is used for tables larger than

2x2. Formula for Cramer’s V:

Nominal Measures: Phi The phi for Problem

12.1 is 0.33. This is a strong

association.

Value Strength

Between 0.0 and

0.10Weak

Between 0.10 and

0.30Moderate

Greater than 0.30

Strong

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.

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.

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

Low High

Low 10 12 22

High 17 5 22

27 17 44

Nominal Measures: Lambda Formula for Lambda:

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%.

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.