Chi-Square Testing
10/23/2012
Readings
•Chapter 7 Tests of Significance and Measures ofAssociation (Pollock) (pp. 155-169)
•Chapter 5 Making Controlled Comparisons (PollockWorkbook)
•Chapter 7 Chi-Square and Measures of Association(Pollock Workbook)
OPPORTUNITIES TO DISCUSSCOURSE CONTENT
Course Learning Objectives
•Students will learn the research methods commonlyused in behavioral sciences and will be able to interpretand explain empirical data.
•Students will learn the basics of research design and beable to critically analyze the advantages anddisadvantages of different types of design.
•As this course fulfills the Computational Skills portionof the University degree plan, students will achievecompetency in conducting statistical data analysis usingthe SPSS software program.
CHI-SQUARE
A test of statistical significance
Why Hypothesis Testing
•To determine whether a relationship existsbetween two variables and did not arise bychance. (Statistical Significance)
•To measure the strength of the relationshipbetween an independent and a dependentvariable? (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 nullhypothesis.
•An insignificant chi-square means that norelationship exists.
Chi-Square is an up or down measure
•If our significance value isless than or equal to.05table, we reject the nullhypothesis- we have arelationship
•if our Chi-Square valuefrom our test is greaterthan .05 we accept thenull hypothesis and wehave no relationship
HOW TO DO IT IN SPSS
An Easy One
•Dataset- NES 2008
•DV= Who08
•IV= Race
•Null- There is norelationship betweenRace and Vote in 2008
•Alternate- AfricanAmericans are Morelikely to Vote for Obama
First Run A Cross Tab
Click onStatistics
Click on Chi-Square
The Results
•What does the Chi-Square Tell us?
•What is the Asymp. Sig here?
•What do We Do with the nullhypothesis?
•What is the Practical Significancehere?
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 nullhypothesis?
•What is the Practical Significancehere?
What do we have Here?
MEASURES OF ASSOCIATION
Nominal Variables
Why Measures of Association
•Chi-Square only tests for significance
•It does not say how strongly the variables arerelated
•We Use a Measure of Association to Do this
A measure of association is a singlenumber that reflects the strengthof the relationship
Measures of association for NominalVariables tell us:
•Strength of theRelationship
•The statisticalsignificance of therelationship
•These go hand in hand
Measures of Association for NominalVariables
Measure ofAssociation
Range
Characteristics
Lambda
0 - 1.0
may underestimate, but aPRE measure
Phi
0 - 1.0
Use for a 2x2 table only andis Chi-square based
Cramer's V
0 - 1.0
Chi-square based and thecompliment to PHI.
A value of 1.00 means a perfectrelationship, a value of .000 means norelationship
Lambda
•What kinds of variablesare needed forLambda?
•Lambda ranges from 0(no relation) to 1 (aperfect relationship)
•It measures how muchbetter one can predictthe value of each caseon the DV if one knowsthe value of the IV
Interpreting Lambda
•.000 to .10 none
•.10-.20 weak
•.20-.30 moderate
•.30-.40 strong
•.40 and above- there is avery strong relationship
Reading Lambda in SPSS
The one in themiddle
The significanceof the Lambda
Lambda as a PRE Measure
•Proportional Reduction in Error (PRE)
•this is defined as the improvement, expressed asa Percentage, in predicting a dependent variabledue to knowledge of the independent variable.
•How well we can predict the dependent variableby 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 PRACTICEEXAMPLES
Problems with Lambda
•It fears a TYPE I error so it is very conservative
•Lambda can Underestimate relationships, evenwhen there are significant chi-square values.
•If the modal category is even, Lambda is prettyuseless.
ALTERNATIVES TO LAMBDA
Phi and Cramer’s V
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, thatwe have a very strong relationship betweenour independent and dependent variables.
Phi And Cramer’s V
Interpreting them
•.000 to .10 none
•.10-.15 weak
•.15-25 moderate
•.25.- 40 strong
•.40 and above- there is avery strong relationship
Limitations
•Neither are PRE Measures
•They are both Chi-squarebased so large samplesinflate it
Lambda Underestimating
What the Cramer’s V Tells Us
•If the Modal category ishard to predict, Lambdafalls flat
•What we see is a weak-to-moderaterelationship here.
•Independents andDemocrats are different
Lambda Underestimating Part II
D.V.- obama_win08
IV- Region
Lambda shows Nothing
We have a moderate relationship, but itis not significant (small sample)
RUNNING LAMBDA, PHI ANDCRAMER’S V
Easy to Do
•How to do it in SPSS
•Analyze
–Descriptive
•Cross-Tabs
–Click on the StatisticsTab
•Highlight your nominalvariable statistics
–Choose continue
Two Examples
Region and Cig Taxes
Region and Public Support forGay Rights
