Path: janda.org/c10 > Syllabus > Topic IX: Ordinal Measures of Association
IX: Topics and Readings: Measures of Association for Discrete, Ordinal Variables

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 "liberal-conservative" ideology -- a seven-point 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 Liberal-Conservative scale R's placement on Liberal-Conservative 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 84-87 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 tau-b and tau-c 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 rank-order correlation coefficient by Spearman
• uses the rank-order 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.