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Correlations PowerPoint PPT Presentation

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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

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BSS Career Fair

  • Wednesday 11/6/2013- Mabee A & B

  • 12:30-2:30P


  • 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

Opportunities to discuss course content

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.

Measures of Association

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 Nominal Variables

Measures of association For Cross-Tabs






  • Strength

  • Significance

Ordinal Measures of Association

Adding a Third Variable

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

Finally Correlations

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

An Example from long ago

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


A Way of Visualizing a Correlation

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!

CO2 and Urban Population

Scatterplots in SPSS

How to do it

  • Graphs

  • Legacy Dialogs

  • Scatter/Dot...

A Window pops up

Select simple

Choose Define

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

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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