PS 225Lecture 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

e

eo

f

ff 22 )(

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 tablesCramer’s V for larger tables

Phi (Φ)

N

2

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

)1,1)(min(

2

crNV

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 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 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. 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.