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PS 225 Lecture 17 Comparing Two Variables In-Class Analysis Independence vs. Dependence Independence: Variables are not related Dependence: Variables demonstrate correlation Independent Variable Dependent Variable Chi-Squared Statistic ( fo fe ) fe 2 2 Hypothesis Test for Independence Ho: Variables are Independent H1: Variables are Dependent SPSS Chi-Square Test Hypothesis Test for Independence Result Reject Ho and conclude H1 : Variables are dependent Don’t Reject Ho : Not enough information to conclude variables are dependent Chi-Squared Test Test for independence Can be used for nominal and ordinal data Nonparametric test Conditional Distribution Extreme Conditional Distributions No Association Perfect Association Measures for Nominal Variables Phi (Φ) for 2x2 tables Cramer’s V for larger tables Phi (Φ) 2 N Phi (Φ) Between 0 and 1 0 No Correlation 1 Perfect Correlation Guidelines for Interpreting Phi Less than 0.10 : Between 0.10 to 0.30 : Greater than 0.30 : Weak Moderate Strong Cramer’s V V 2 ( N )(min r 1, c 1) Cramer’s V Between 0 and 1 0 No Correlation 1 Perfect Correlation Guidelines for Cramer’s V Less than 0.10 : Between 0.10 to 0.30 : Greater than 0.30 : Weak Moderate Strong Measures for Nominal Variables Phi (Φ) for 2x2 tables Cramer’s V for larger tables Measures for Ordinal Variables Gamma- for collapsed ordinal variables Spearman’s Rho – for continuous ordinal variables Gamma Increase in accuracy of prediction 0-0.3 weak 0.31 to 0.6 moderate Greater than 0.61 strong Sign indicates strength Spearman’s Rho Proportionate Reduction in Error (PRE) Robert Putnam Political Scientist at Harvard University Studies Social Capital, “features of social lifenetworks, norms and trustthat enable participants to act together effectively to pursue shared objectives” Reading for Next Class Get Article from JSTOR Tuning In, Tuning Out: The Strange Disappearance of Social Capital in America Robert D. Putnam PS: Political Science and Politics, Vol. 28, No. 4. (Dec., 1995), pp. 664-683. SPSS Assignment What characteristics of individuals might increase or decrease the likelihood they will engage in activities that build social capital like visiting neighbors (socommun2) or friends (socfrend2)? Choose three survey responses to study Conduct a Chi-Squared hypothesis test for independence Give your hypotheses, test results and interpretation Characterize the relationship using a measure of association Clearly indicate which measure you use and give the relative size of the impact of the independent variable.