Significance Testing 10/22/2013

Readings Chapter 3 Proposing Explanations, Framing Hypotheses, and Making Comparisons (Pollock) (pp ) Chapter 5 Making Controlled Comparisons (Pollock) Chapter 4 Making Comparisons (Pollock Workbook)

OPPORTUNITIES TO DISCUSS COURSE CONTENT

Office Hours For the Week When – Wednesday – Thursday 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.

Hypothesis Testing

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 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!

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)!

Errors and Decisions

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

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.

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 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

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! Accept or Reject the Null? Is this value less than.05?

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. Accept or Reject the Null?

Global Warming Policy and Views on the Tea Party (2010) Accept or Reject the Null?

What do we have Here?

The 2010 Election In Texas

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 Tab Click 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?

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

The one in the middle The significance of the Lambda 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.