Chi-Square Testing 10/16/2012

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 – Friday 10-11 – Monday 8-10 – And appointment

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.

Hypothesis Testing

Variables • Dependent Variable- the variable/result that you want to explain. • Independent Variable(s)- the variables that you believe will cause/explain/change your dependent variable

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)

TESTING FOR STATISTICAL SIGNIFICANCE

What is Statistical Significance?

• Saying that an observed relationship really exists and is not happening by chance • It doesn't mean the finding is important or that it has any real world application (beware of large samples) • Practical significance

Determining Statistical Significance • Establishing parameters or “confidence intervals” • Are we confident that our relationship is not happening by chance?

• We want to be rigorous (we usually use the 95% confidence interval)

How do We establish confidence • Establishing a “p” value or alpha value • This is the amount of error we are willing to accept and still say a relationship exists

P-values or Alpha levels • p<.05 (95% confidence level) - There is less than a 5% chance that we will be wrong. • p<.01. (99% confidence level) 1% chance of being wrong • p<.001 (99.9 confidence level) 1 in 1000 chance of being wrong

Problems of the Alpha level (p-value) • Setting it too high • Setting it too low • We have to remember our concepts and our units of analysis

You should always use the 95% Confidence interval (p<.05) unless there is a good reason not to.

STATING HYPOTHESES

Testing a hypothesis • Before we can test it, we have to state it – The Null Hypothesis- There is no relationship between my independent and dependent variable –

The Alternate Hypothesis

• We are testing for Significance: We are trying to disprove the null hypothesis and find it false!

More on the Alternate Hypothesis • Also called the research hypothesis • State it clearly • State an expected direction

After testing, the Null is either • True- no relationship between the groups, in which case the alternate hypothesis is false--- Nothing is going on (except by chance)! • False- there is a relationship and the alternative hypothesis is correct-- something is going on (statistically)!

It seems pretty obvious whether or not you have a statistically significant relationship, but we can often goof things up.

DECISION TYPES AND ERRORS

Errors and Decisions

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

false alarm)

– Spam Filters that eat good mail – – Any Diagnosis on WebMD The entire premise of Hang em high

A Type II error •

A Type II Error-

accepting a null hypothesis when it should have been rejected. (denial) – Austin Traffic

Type I and II (Climate Change)

A test of statistical significance

CHI-SQUARE

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.

How to tell a relationship • 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. We want patterns

No Variation

Significant Variation

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

An Example •

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.

Chi-Square in SPSS • Pearson-Chi Square – Value (bigger is more likely to be significant) – D.F. (Degrees of freedom, the size of the table) • Asymp. Sig (2-sided) This is the column that matters!

• •

Role of Women and Marital Status

Null- There is no relationship between marital status and beliefs on the role of women Alternate- Married people will be more likely to say female role at home.

Global Warming Policy and Views on the Tea Party (2010)

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

Click on Statistics First Run A Cross Tab 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?