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### Correlations

### Finally Correlations

11/5/2013

BSS Career Fair

- Wednesday 11/6/2013- Mabee A & B
- 12:30-2:30P

Readings

- Chapter 8 Correlation and Linear Regression (Pollock) (pp. 182-187)
- Chapter 8 Correlation and Regression (Pollock Workbook)

Homework Due 11/7

- Chapter 7 Pollock Workbook
- Question 1
- A, B, C, D, E, F

- Question 2
- A, B, C, D

- Question 3 (use the dataset from the homework page)
- A, B, C, D

- Question 5
- A, B, C D, E

- Question 1

Office Hours For the Week

- When
- Wednesday10-12
- Thursday 8-12
- And by appointment

Course Learning Objectives

- Students will be able to interpret and explain empirical data.
- Students will achieve competency in conducting statistical data analysis using the SPSS software program.

Why Hypothesis Testing

- To determine whether a relationship exists between two variablesand did not arise by chance. (Statistical Significance)
- To measure the strength of the relationship between an independent and a dependent variable? (association)

Measures of association For Cross-Tabs

Nominal

Ordinal

Strength

Significance

Direction!

- Strength
- Significance

How to Control for a Variable?

A Third Variable

- the relationship between two variables may be spurious, weak or even too strong
- "controlling" for a third variable is a method of removing or separating the effects of another variable.
- This gets at the underlying relationship

Why Add the Third Variable

- Is there an antecedent variable at play?
- Is the observation different for different groups of people

Marijuana and a Third Variable

- H1: People with children will have different views on legalization than others of the same ideology
- Cross-tabs
- Input Row Variable
- Input Column Variable
- To control for a variable place it in the area that says Layer 1 of 1.

Views on Homosexuality, Party ID and Race

- DV- homosex2
- IV- partyid3
- Control- race 2

You have been waiting to use this

What is correlation?

- Any relationship between two variables
- Correlation does not mean causation

What Could Be Happening?

- Variable A influences variable B
- Variable B influences variable A
- It is a coincidence
- Some other variable (C) influences both A and B

Correlation Coefficients

Note the lower case r

- Pearson’s Product Movement (Pearson’s r)
- A way of measuring the goodness of fit between two continuous variables

Rules on Correlations

- Variables must be continuous.
- You cannot use ordinal or nominal variables here
- Small samples >30 can give you odd results

Measuring Pearson’s r

- Measure from -1 to 0 to 1.
- -1 means a perfect negative relationship
- 0 is the absence of any relationship
- +1 is a perfect positive relationship

- Like Somers’ D, Pearson's "r" scores tell us
- Direction
- Strength of Association
- Statistical significance of the measure

PEARSON'S r's are PRE Measures!

- Squaring the (r) value provides a measure of how much better we can do in predicting the value of the d.vby knowing the independent variable.
- We call this a r2(r-square) value.

Significance and Strength

- Significance Levels: We use the .05 level
- Count your Stars(if available)
- *=significant at .05
- **= significant at.01
- No Stars= No Significance

- Relationship strengths of r-square values
- .000 to .10 = none-
- .11-.20 weak-moderate
- .20-.35 moderate
- .35-.50 moderate- strong
- .50 there is a strong relationship

The Previous Example

- We Square the correlation value .733
- This gives us a value of .537 (r-square)

- From this we can say 53.7% (PRE) of the variation in the dependent variable can be explained by the independent variable
- We cannot, however, say that being Baptist increases the syphilis rate.

American Cities

- Violent Crime Rate, Teen Unemployment Rate, Roadway congestion, Heart Disease

World Health Indicators

- Coal consumption , Adequate Sanitation, Child Mortality, Child Immunization

Correlations in SPSS

- Analyze
- Correlate
- Bivariate

- You can include multiple variables

More on Scatterplots

- We can think of this line as a prediction line.
- The closer the dots to the line, the stronger the relationship, the further the dots the weaker the line.
- If all the data points are right on the regression line, then there is a perfect linear relationship between the two variables.
- This only graphs a correlation...... this means that it does not mean causality nor should it be used for testing!

How to do it

- Graphs
- Legacy Dialogs
- Scatter/Dot...

Adding Case Labels

- put your variable in the Label Cases by area
- Click on Options, and this will open up a window
- Click on display chart with case labels and continue
- Click OK

- Click on display chart with case labels and continue

Including a fit Line with your Scatterplot

Do not use scatterplots for testing! There are better measures, especially if you have more than 1 iv. (your paper should not include any scatterplots)

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