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.

CHI-SQUAREA test of statistical significance

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 TabClick on Statistics 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 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?

MEASURES OF ASSOCIATIONNominal Variables

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 Characteristics

Lambda 0 - 1.0may underestimate, but a PRE measure

Phi 0 - 1.0Use for a 2x2 table only and is Chi-square based

Cramer's V 0 - 1.0Chi-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.

ALTERNATIVES TO LAMBDAPhi 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, that we have a very strong relationship between our 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 a very strong relationship

Limitations• Neither are PRE Measures

• 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 weak-to-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 TaxesRegion and Public Support for Gay Rights