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Analyzing Independence and Dependence of Variables: A Comprehensive Guide

This lecture focuses on the analysis of the relationship between two variables, exploring the concepts of independence and dependence. You'll learn about independent and dependent variables, the Chi-Squared statistic, and hypothesis testing for independence. The criteria for rejecting or not rejecting the null hypothesis are explained. Additionally, measures for nominal and ordinal variables, such as Phi, Cramer’s V, and Spearman’s Rho, are discussed. The session includes a practical SPSS assignment to analyze social capital using provided survey responses.

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Analyzing Independence and Dependence of Variables: A Comprehensive Guide

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  1. PS 225Lecture 17 Comparing Two Variables

  2. In-Class Analysis

  3. Independence vs. Dependence • Independence: Variables are not related • Dependence: Variables demonstrate correlation • Independent Variable • Dependent Variable

  4. Chi-Squared Statistic

  5. Hypothesis Test for Independence • Ho: Variables are Independent • H1: Variables are Dependent

  6. SPSS Chi-Square Test

  7. 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

  8. Chi-Squared Test • Test for independence • Can be used for nominal and ordinal data • Nonparametric test

  9. Conditional Distribution

  10. Extreme Conditional Distributions • No Association • Perfect Association

  11. Measures for Nominal Variables • Phi (Φ) for 2x2 tables • Cramer’s V for larger tables

  12. Phi (Φ)

  13. Phi (Φ) • Between 0 and 1 • 0 No Correlation • 1 Perfect Correlation

  14. Guidelines for Interpreting Phi • Less than 0.10 : Weak • Between 0.10 to 0.30 : Moderate • Greater than 0.30 : Strong

  15. Cramer’s V

  16. Cramer’s V • Between 0 and 1 • 0 No Correlation • 1 Perfect Correlation

  17. Guidelines for Cramer’s V • Less than 0.10 : Weak • Between 0.10 to 0.30 : Moderate • Greater than 0.30 : Strong

  18. Measures for Nominal Variables • Phi (Φ) for 2x2 tables • Cramer’s V for larger tables

  19. Measures for Ordinal Variables • Gamma- for collapsed ordinal variables • Spearman’s Rho – for continuous ordinal variables

  20. Gamma • Increase in accuracy of prediction • 0-0.3 weak • 0.31 to 0.6 moderate • Greater than 0.61 strong • Sign indicates strength

  21. Spearman’s Rho • Proportionate Reduction in Error (PRE)

  22. 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”

  23. 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.

  24. 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.

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