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

Hypothesis Test for Independence  H o : Variables are Independent  H 1 : Variables are Dependent

SPSS Chi-Square Test

Hypothesis Test for Independence Result  Reject H o and conclude H 1 : Variables are dependent  Don’t Reject H o : 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)

 Between 0 and 1  0 No Correlation  1 Perfect Correlation

Guidelines for Interpreting Phi  Less than 0.10 : Weak  Between 0.10 to 0.30 : Moderate  Greater than 0.30 : Strong

Cramer’s V

 Between 0 and 1  0 No Correlation  1 Perfect Correlation

Guidelines for Cramer’s V  Less than 0.10 : Weak  Between 0.10 to 0.30 : Moderate  Greater than 0.30 : 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  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 life- networks, norms and trust- that 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

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.