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PS102Lecture20 - Measures of Association Political Science...

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Measures of Association Political Science 102 Introduction to Political Inquiry Lecture 20
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Why Use Measures of Association? Cross-tabs and scatter plots are flexible tools for exploring relationships between variables Chi-squared test evaluates statistical significance Neither method provides a summary measure of the relationship What is the direction? How strong is the relationship? Measures of Association seek to provide this information
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Ordinal Linear Measures Coefficient compares pairs of cases record them as concordant, discordant, or tied Concordant – case 1 is higher (or lower) than case 2 on both X and Y Discordant – case 1 is lower than case 2 on X, but higher than case 2 on Y (or vice versa) Tied – case 1 and case 2 are equal on either X, or Y, or both Positive coefficient indicates more concordant than discordant pairs & negative coefficient indicates more discordant pairs than condordant
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Ordinal Linear Measures Coefficients vary in how they weight and account for ties Gamma ignores ties (may ignore much of the data) Tau-b uses a weighted average of ties on X and Y All of these coefficients focus on linear relationships (or at least monotonic) Curvilinear and contingent relationships may be masked by these procedures
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Goodman & Kruskal’s Gamma γ = C - D C + D
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