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SOC 325
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Sociology

SOC 325

Elizabeth Quinlan

Winter

Description

Soc 325
March 10 2014
1
Measures of Association for Ordinal Variables Chapter 12
What we are going to cover today
•If you're working with a mixture of variables (one nominal one ordinal) what measure of
association do you use?
o Come down to the lowest level of measurement in the mixed bivariate
association and work with the measures of association that works with it
•2 types of ordinal variables
•Measures of strength of an association for ordinal variables
•
Determining the direction of relationships
•Testing these measures for statistical significance
Two types of Ordinal variables:
o Collapsed: no more than 5-6 categories
•
Can have 2, 3, 4, 5, 6
• Will create a bivariate table
• Gamma (G) is measure of association for a 2 ordinal level variables that
have been arranged in a bivariate table
Symmetric measure -- same value regardless of which is independent,
which is dependent
PRE Measure (Proportional Reduction in Error) measure of association,
based on the logic of the "similar and dissimilar pairs of cases"
• Your predictive power increases if you have knowledge of the
independent variable
• Examples:
• Similar pair:
Education Income
Joseph high high
Steven low low
• Joseph has a high level of education and a high
level of income whereas steven has a low level of
education and low level of income
• For this "pair" of cases
• Joseph reports a higher level of education
than Steven AND Joseph also reporst a higher level
of income than Steven
• Dissimilar pair:
Education Income
Carole high low
Matt low high
• Ordering is not the same
• For this "pair" of cases
• Carole reports a higher level of education
than Matt but Carole has a lower level of income
than Matt
Number of pairs: N(n-1)
2 Soc 325
March 10 2014
2
• If N was 50 the number of pairs would be
1,225 which is a lot of cases
• Tied pairs:
• Gamma ignores all tied pairs of casses
education income
Joseph high high
Steve high low
• Pairs that are tied on the independent variable
• Pairs that are tied on the dependent variable
• Pairs tied on both the independent variable and the
dependent variable
• Gamma is computed with formula 12.2:
N
G= s−Nd
N sN d
• It ranges from 0 (no association) to ±1.00 (perfect
association)
• As the excess of similar pairs increases (N S >ND)amma increases
and is a positive value
• As the excess of dissimilar pairs increases (N D > S )ma
increases and is a negative value
• Table 12.3 provides a guide to interpret the strength of gamma
Absolute Value Strength
If the value is: The strength of the relationship is
between 0.00 and 0.10 weak
between 0.11 and 0.30 moderate
greater than 0.30 strong
• A positive relationship, measures of association ±1
•
For example: in our survey investigating the relationship
between education (ind) and income (dep) G= +.71 we
conclude
• The relationship is a strong and positive one: as education
increases income increases
• When predicting the order of pairs of cases on the
dependent variable (income), we would make 71% fewer
errors by taking the independent variable (education) into
account
• Limitations of gamma
1. When variables are not coded from l

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