Measures of Association in SPSS 10
This crosstabs table
below relates two discrete, ordinal variables
 The dependent variable
is "Party ID"  a seven scale ranging from 0 to 6 in the
2000 NES survey
 The independent variable
is "liberalconservative" ideology  a sevenpoint scale
ranging from 1 to 7
 The two variables are
obviously related; what's the appropriate measure of
relationship?
Crosstabulation
 K1x. PARTY ID SUMMARY by R's placement on
LiberalConservative scale


R's placement on
LiberalConservative scale

Total

K1x.
PARTY ID SUMMARY

extremely
liberal

liberal

slightly
liberal

moderate

slightly
conservative

conservative

extremely
conservative


Strong
Democrat

7

35

24

32

10

15

1

124

Weak
Democrat

2

13

17

38

11

8


89

Ind
Democrat

6

16

21

46

7

11


107

Independent


4

8

30

9

10

3

64

Ind
Republican


4

7

32

30

15

6

94

Weak
Republican

1

2

6

24

29

24

6

92

Strong
Republican


1

2

12

17

57

10

99

Total

16

75

85

214

113

140

26

669

SPSS Users' Guide on page 8487 describes several
measures of association:
 The gamma
coefficient by Goodman and Kruskal
 computes the
difference between "discordant" and "concordant" ranks
among every pair of cases
 The taub and
tauc coefficients by Kendall
 works much like
gamma, except that cases tied on ranks are treated
differently
 The d coefficient
by Somers
 an asymmetric
extension of gamma, in which each variable is treated
as dependent.
 The rankorder
correlation coefficient by Spearman
 uses the rankorder
of each variable in computing the Pearson product
moment correlation
 The regular
Pearson product moment correlation itself.
Here's the SPSS output from the above table, asking for
all ordinal measures
Why are there so many different measures to supplement
the Pearson correlation?
 Because all of them have
weaknesses  which we will not cover
 It's sufficient for our
course to note that there are alternative measures
of association for ordinal data
 These measures were
created to deal with the nature of ordinal data
 The values on an
ordinal scale reflect magnitude
 But we do not know
the distances between values on an ordinal
scale
 Thus, the Pearson
correlation coefficient is
inappropriate
 We need measures
of association designed for ordinal
variables.
 But according to the
argument in Labovitz's article
 It doesn't make much
difference what the "true" distances are,
 as long as one
preserves monotonicity in scoring the
variables
 That is, match the
magnitude of the scores to the order of the
values
 Intercorrelations
among ordinal variables with widely different scoring
schemes are still high
 According to his
argument, which I endorse, just compute Pearson's
r for ordinal data.
