This preview shows pages 1–8. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Measures of Association Political Science 102 Introduction to Political Inquiry Lecture 20 Why Use Measures of Association? Crosstabs and scatter plots are flexible tools for exploring relationships between variables Chisquared 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) Taub 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 TauB 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...
View
Full
Document
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.
 Spring '11
 Gelpi
 Political Science

Click to edit the document details