### PS 225 Lecture 9

```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
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”
 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.
```