Chi-Square Testing
10/23/2012
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
– Thursday 8-12
– Wednesday 11-1
– And appointment
• The endorsement
Course Learning Objectives
• Students will learn the research methods commonly
used in behavioral sciences and will be able to interpret
and explain empirical data.
• Students will learn the basics of research design and be
able to critically analyze the advantages and
disadvantages of different types of design.
• 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.
A test of statistical significance
CHI-SQUARE
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)
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 significance value is
less than or equal to.05
table, we reject the null
hypothesis- we have a
relationship
• if our Chi-Square value
from our test is greater
than .05 we accept the
null hypothesis and we
have no relationship
HOW TO DO IT IN SPSS
An Easy One
• Dataset- NES 2008
• DV= Who08
• IV= Race
• Null- There is no
relationship between
Race and Vote in 2008
• Alternate- African
Americans are More
likely to Vote for Obama
First Run A Cross Tab
Click on
Statistics
Click on ChiSquare
The Results
• What does the Chi-Square Tell us?
• What is the Asymp. Sig here?
• What do We Do with the null
hypothesis?
• What is the Practical Significance
here?
Hard-Line Immigration Policy
• D.V. Immigration Policy
• I.V. Hispanic
(dichotomous)
The Results
• What does the Chi-Square Tell us?
• What is the Asymp. Sig here?
• What do We Do with the null
hypothesis?
• What is the Practical Significance
here?
What do we have Here?
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
The one in the
middle
The significance
of the Lambda
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 predict 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.
SOME LAMBDA PRACTICE
EXAMPLES
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.
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
An Example
• Here we can say with a .369 Cramer's V, that
we have a very strong relationship between
our independent and dependent variables.
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
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
• 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