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march 10.docx

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Department
Sociology
Course
SOC 325
Professor
Elizabeth Quinlan
Semester
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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