PS102Lecture20

PS102Lecture20 - Measures of Association Political Science...

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Unformatted text preview: Measures of Association Political Science 102 Introduction to Political Inquiry Lecture 20 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 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 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 Goodman & Kruskal’s Gamma γ = C- D C + D C = Concordant pairs D = Discordant pairs C = 23 x 68 = 1,564 D = 5 x 3 = 15 Tx = (23 x 5) + (3 x 68) Ty = (23 x 3) + (5 x 68) Goodman & Kruskal’s Gamma γ = C- D C + D C = 23 x 68 = 1,564 D = 5 x 3 = 15 Tx = (23 x 5) + (3 x 68) = 319 Ty = (23 x 3) + (5 x 68) = 409 γ = 1564 - 15 1564 +15 = 0.98 Kendall’s Tau-B C = 23 x 68 = 1,564 D = 5 x 3 = 15 Tx = (23 x 5) + (3 x 68) = 319 Ty = (23 x 3) + (5 x 68) = 409 τ b = C- D ( C + D + T y ) ´ C + D + T x τ b = 1564 - 15 1564 +15 + 409 ´ 1564 +15 + 319 = 0.797 Linearity and the Limits of...
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This note was uploaded on 10/21/2011 for the course POL SCI 102 taught by Professor Gelpi during the Spring '11 term at Duke.

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PS102Lecture20 - Measures of Association Political Science...

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