POLS-3328 Fall 2010-- Lecture Outline

October 19, 2010


Cross-Tabs and Chi Square

Readings:

Chapter 11 Statistics First Steps (Johnson and Reynolds) (pp. 393-420) 
Chapter 7 Tests of Significance and Measures of Association (Pollock) (pp. 145-162) 
Chapter 5 Making Controlled Comparisons (Pollock Workbook) 
Chapter 7 Chi-Square and Measures of Association (Pollock Workbook)


Today's Lecture

COURSE LEARNING OBJECTIVES

  1. Students will learn the research methods commonly used in behavioral sciences and will be able to interpret and explain empirical data.

  2. Students will achieve competency in conducting statistical data analysis using the SPSS software program

CROSS-TABULATIONS

Hypothesis Testing With Cross-Tabulations

The purpose of hypothesis testing is to determine whether a relationship exists between two variables. 

  1. What is the probability that a particular finding arose by chance? 

  2. How strong is the relationship between an independent and a dependent variable?

Types of Hypotheses

  • A Type I Error- the incorrect or mistaken rejection of a true null hypothesis (a false alarm)

  • A Type II Error- failing to reject a null-hypothesis when it should have been rejected. (denial)

 

The CHI-SQUARE TEST

This is a procedure for evaluating the level of statistical significance attained by a bivariate relationship in a cross-tabulation.

What is Chi-Square

  • It is a test of significance between two variables.  

    • If there is no-relationship, all the values will be dispersed evenly throughout the cells

    • If there is a relationship, a pattern will appear in the cells 

  • FOR A CHI SQUARE VALUE TO BE SIGNIFICANT, THERE HAS TO BE A LOT OF VARIATION IN THE TABLE! WE WANT TO SEE THE UNEXPECTED.

How to Tell if we have a significant Chi-Square

  • Alpha Level (our level of significance)

  • Degrees of Freedom- (how many cells in our cross-tab)  


     

  • Critical Chi-Square value- the minimum value of chi-square needed to demonstrate a significant relationship 

  • A Chi-Square Table

    • if our Chi-Square value from our test  is greater than or equal to the Critical value from the table, we reject the null hypothesis-  we have a relationship

    • if our Chi-Square value from our test  is less than the Critical Value from the table, we accept the null hypothesis and we have no relationship

Example 1-  Church attendance and Sex Ed

Null Hypothesis-  There is no relationship between church attendance and belief in teaching sex ed in the schools
Alternate Hypothesis-  As religious attendance increases, people are more likely to oppose sex education in the public schools. 

Using the Table

  • What is the minimum value of chi square necessary for significance. 

  • Based on our Pearson Chi-Square, what do we do with the Null, and why?

Example 2-  Gun Ownership and Confidence in Congress

Null Hypothesis-  There is no relationship between gun ownership and Confidence in Congress
Alternate Hypothesis-  Gun owners are less trusting of Congress than non-gun owners.

 

Example 3-  Extra-Marital Sex and Marital Status

Null Hypothesis- There is no relationship between marital status and support for extra-marital sex
Alternate Hypothesis- Married people will be more likely to say that extra-marital sex is always wrong

How to do this in SPSS

From the Congress Data Set Here is My alternate Hypothesis: Older Congressmen will have less education because they grew up in a time when Post High-School education was not available or affordable. 

  • What does the Chi-Square Tell us? 

  • What is the Asymp. Sig here?

  • What do We Do with the null hypothesis?

One To Try Out with the NES 2004

  • IV= Attend3

  • DV= Bible

A Chi-Square tests gives us two things

  • A Chi-Square value - listed below as Pearson Chi-Square

  • A significance level- listed as Asymp. Sig

  1. The higher our value, the stronger our significance.

  2. The Lower our ASYMP.SIG the stronger our significance

    • .000 means there is a 1 in 1000 chance of accepting a false null hypothesis.

    • we accept anything less than .05

 

Limitations of Chi-Square Values




This page maintained by Brian William Smith
To the lecture notes page