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.
 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.
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:
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
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
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
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.
Nominal Measures: Lambda
 Formula for Lambda:
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
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
Low
Author.
High
Author.
Totals
Low Efficiency
10
12
22
High Efficiency
17
5
22
Totals
27
17
44
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%.
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.
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%)
Totals
27(100%)
17(100%)
44(100%)