Cross-Tabs With Nominal
Variables
10/24/2013
Readings
• Chapter 7 Tests of Significance and Measures
of Association (Pollock) (pp. 155-169)
• Chapter 5 Making Controlled Comparisons
(Pollock Workbook)
• Chapter 7 Chi-Square and Measures of
Association (Pollock Workbook)
OPPORTUNITIES TO DISCUSS
COURSE CONTENT
Office Hours For the Week
• When
– Friday 10-11
– Monday 10-12
– Tuesday 8-12
– And by appointment
Course Learning Objectives
1. Students will be able to interpret and explain
empirical data.
2. Students will achieve competency in
conducting statistical data analysis using the
SPSS software program.
A test of statistical significance
CHI-SQUARE
What is Chi-Square?
• A test of significance
between two
categorical variables
• We run the test in
conjunction with crosstabs
Things about Chi-Square
• It is not a test of strength, just significance
• Chi-square is inflated by large samples
• It is a test that tries to disprove the null
hypothesis.
• An insignificant chi-square means that no
relationship exists.
Chi-Square is an up or down measure
• if our Chi-Square
significance value from
our test is greater than
.05 we accept the null
hypothesis and we have
no relationship
• If our significance value is
less than or equal to.05
table, we reject the null
hypothesis- we have a
relationship
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 tell us:
• Strength of the
Relationship
• The statistical
significance of the
relationship
• These go hand in hand
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.
A value of 1.00 means a perfect
relationship, a value of .000 means no
relationship
Lambda
• What kinds of variables
are needed for
Lambda?
• Lambda ranges from 0
(no relation) to 1 (a
perfect relationship)
• It measures how much
better one can predict
the value of each case
on the DV if one knows
the value of the IV
Interpreting Lambda
• .000 to .10 none
• .10-.20 weak
• .20-.30 moderate
• .30-.40 strong
• .40 and above- there is a
very strong relationship
Reading Lambda in SPSS
• IN SPSS, LAMBDA GIVES YOU 3 DIFFERENT
VALUES
• Symmetric- always ignore
• Two measures of your dependent variable
– always use the lambda associated with your
dependent variable.
– If you place the dependent variable as the ROW
VARIABLE, this will be the middle value.
• Help from Rocky IV- And the video
Lambda Significance Value
• The P-value for the test statistic (p<.05)
• Is the association real or happening by
chance?
The one in the
middle
Ignore these
The significance
of the Lambda
p<.05
Lambda as a PRE Measure
• Proportional Reduction in Error (PRE)
• this is defined as the improvement, expressed as
a Percentage, in predicting a dependent variable
due to knowledge of the independent variable.
• How well we can increase our prediction of the
dependent variable by knowing the independent
variable?
Converting a Lambda to a Percent
• We take the value of our association measure
• Multiply by 100%
• this is our PRE value.
Problems with Lambda
• It fears a TYPE I error (false
alarm) so it is very
conservative
• Lambda can Underestimate
relationships, even when
there are significant chisquare values.
• If the modal category is even,
Lambda is pretty useless.
SOME LAMBDA PRACTICE
EXAMPLES
Fracking and the Northeast
30%
25%
20%
15%
10%
5%
0%
NE
MW
S
W
Phi and Cramer’s V
ALTERNATIVES TO LAMBDA
Cramer’s V
• An alternative to Lambda
• Ranges from 0 -1.0
• Not a Pre Measure
Phi
• Measured similarly to Lambda
• You will use this with 2x2 tables only
Phi And Cramer’s V
Interpreting them
• .000 to .10 none
Limitations
• Neither are PRE Measures
• .10-.15 weak
• .15-25 moderate
• .25.- 40 strong
• .40 and above- there is a
very strong relationship
• They are both Chi-square
based so large samples
inflate it
An Example
• Here we can say with a .369 Cramer's V, that
we have a strong relationship between our
independent and dependent variables.
Lambda Underestimating
What the Cramer’s V Tells Us
• If the Modal category is
hard to predict, Lambda
falls flat
• What we see is a weakto-moderate
relationship here.
• Independents and
Democrats are different
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