Transcript Political Research and Statistics

Measures of Association
10/25/2012
Readings
• Chapter 7 Tests of Significance and Measures of
Association (Pollock) (pp. 169-179)
• Chapter 11 Doing Your Own Political Analysis (Pollock
Workbook)
Homework
• Due 10/30/2012
• Chapter 4: Pollock Workbook
– Question 1
• A, B, C, D
– Question 3
• A, B
– Question 5
• A, B, C, D (a line chart, follow instructions in workbook)
– Question 7
• A, B, C
OPPORTUNITIES TO DISCUSS
COURSE CONTENT
Office Hours For the Week
• When
– Friday 11-1
– Monday 11-1
– Tuesday 8-12
– And appointment
Course Learning Objectives
• Students will be able to interpret and explain
empirical data.
• As this course fulfills the Computational Skills
portion of the University degree plan,
students will achieve competency in
conducting statistical data analysis using the
SPSS software program.
Why Hypothesis Testing
• To determine whether a relationship exists
between two variables and did not arise by
chance. (Statistical Significance)
• To measure the strength of the relationship
between an independent and a dependent
variable? (association)
Nominal Variables
MEASURES OF ASSOCIATION
Why Measures of Association
• Chi-Square only tests for significance
• It does not say how strongly the variables are
related
• We Use a Measure of Association to Do this
A measure of association is a single
number that reflects the strength
of the relationship
Measures of Association for Nominal
Variables
Measure of
Association
Range
Lambda
0 - 1.0
Phi
0 - 1.0
Cramer's V
0 - 1.0
Characteristics
may underestimate, but a
PRE measure
Use for a 2x2 table only and
is Chi-square based
Chi-square based and the
compliment to PHI.
Problems with Lambda
• It fears a TYPE I error so it is very conservative
• Lambda can Underestimate relationships, even
when there are significant chi-square values.
• If the modal category is even, Lambda is pretty
useless.
Lambda Underestimating Part II
D.V.- obama_win08
IV- Region
Lambda shows Nothing
We have a moderate relationship, but it
is not significant (small sample)
RUNNING LAMBDA, PHI AND
CRAMER’S V
Easy to Do
• How to do it in SPSS
• Open States.SAV
• Analyze
– Descriptive
• Cross-Tabs
– Click on the Statistics
Tab
• Highlight your nominal
variable statistics
– Choose continue
Two Examples
Region and Cig Taxes
Region and Public Support for
Gay Rights
Open up the GSS and Try one for
yourself
ORDINAL VARIABLES
Dichotomous Variables
• When a variable takes
on two values
• In cross-tabs, you can
treat dichotomous
variables as ordinal!
Measures of association
Nominal
• Strength
Ordinal
• Strength
• Significance
• Significance
• Direction!
For Ordinals
• strength (measured as the distance away from
zero)
• significance (measured at the .05 level)
• direction- This allows us to determine if we
have a positive or negative relationship
between our variables.
Ordinal Measures of Association
Measure
Range
Characteristics
Gamma
-1.0 to 1.0
Tends to be generous
Kendall's Tau B
-1.0 to 1.0
For square tables
Kendall's Tau C
-1.0 to 1.0
For rectangular
Somers’ D
-1.0 to 1.0
Our preferred measure
About these measures
• all three are PRE measures.
• each has a possible range of -1 to 1. As we
approach -1 or 1 the stronger our relationship.
A value of 0 (zero), means no relationship.
• A positive number indicates a positive
relationship, a negative value means a
negative relationship.
Somers’ D
Why D?
• You are able to test a
specific dependent variable
• It works for both square and
rectangular tables
• Use the one in the middle
Relationship Strengths
• Guidelines
–
–
–
–
–
–
Under .1- very weak
.10 and .15 weak
.15 and .25 moderate
.25-35 moderate-strong
.35-.45 strong
Above .45 very strong
A POSITIVE RELATIONSHIP
• changes in the IV are associated with changes
in the same direction for the DV. As the
numbers of the IV increase, the numbers in
the DV increases.
How it looks in a cross-tab
• As people believe abortion should be more
available, 1===>3. They are more likely to vote
for Obama (0 to 1).
A NEGATIVE RELATIONSHIP
• Changes in the IV are associated with changes
in the reverse direction in the DV. As the
numbers increase in the IV., the numbers in of
the DV decrease
In SPSS
• As states become more democratic (1-3), they
have fewer abortion restrictions (3 to 1)
An Example
The Measures of Association
A negative value does not
mean a weak relationship.
LOOK AT THE ABSOLUTE
VALUE!!!!
GDP and Democracy
An Example
• Maurice Duverger (1957) wrote that "the simple-majority single-ballot
system favors the two-party system" and that "multimember districts
favor multiple parties". Hypothesis- PR systems will have more parties
– D.V. -enpp3_democ (Effective number of parliamentary parties: 3 cats)
– IV- pr_sys (PR system)