Cross-Tabs With Nominal Variables 10/24/2013

Readings Chapter 7 Tests of Significance and Measures of Association (Pollock) (pp ) 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 – Monday – 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.

CHI-SQUARE A test of statistical significance

What is Chi-Square? A test of significance between two categorical variables We run the test in conjunction with cross- tabs

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

MEASURES OF ASSOCIATION Nominal 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 AssociationRangeCharacteristics Lambda may underestimate, but a PRE measure Phi Use for a 2x2 table only and is Chi-square based Cramer's V 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 weak moderate 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 videovideo

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 The significance of the Lambda p<.05 Ignore these

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 chi- square values. If the modal category is even, Lambda is pretty useless.

SOME LAMBDA PRACTICE EXAMPLES

Fracking and the Northeast

ALTERNATIVES TO LAMBDA Phi and Cramer’s V

Cramer’s V An alternative to Lambda Ranges from 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 weak moderate 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

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 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 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