Correlations
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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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Correlations

Correlations

11/5/2013


Bss career fair

BSS Career Fair

  • Wednesday 11/6/2013- Mabee A & B

  • 12:30-2:30P


Readings

Readings

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

  • Chapter 8 Correlation and Regression (Pollock Workbook)


Homework due 11 7

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

Opportunities to discuss course content


Office hours for the week

Office Hours For the Week

  • When

    • Wednesday10-12

    • Thursday 8-12

    • And by appointment


Course learning objectives

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

Measures of Association


Why hypothesis testing

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 Nominal Variables


Measures of association for cross tabs

Measures of association For Cross-Tabs

Nominal

Ordinal

Strength

Significance

Direction!

  • Strength

  • Significance


Ordinal measures of association

Ordinal Measures of Association


How to control for a variable

Adding a Third Variable

How to Control for a Variable?


A third 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

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

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

Views on Homosexuality, Party ID and Race

  • DV- homosex2

  • IV- partyid3

  • Control- race 2


Finally correlations

Finally Correlations

You have been waiting to use this


What is correlation

What is correlation?

  • Any relationship between two variables

  • Correlation does not mean causation


What could be happening

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

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

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

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

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 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

An Example from long ago


The previous example

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

American Cities

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


World health indicators

World Health Indicators

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


Correlations in spss

Correlations in SPSS

  • Analyze

    • Correlate

    • Bivariate

  • You can include multiple variables


Scatterplots

Scatterplots


A way of visualizing a correlation

A Way of Visualizing a Correlation


More on scatterplots

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

CO2 and Urban Population


Scatterplots in spss

Scatterplots in SPSS


How to do it

How to do it

  • Graphs

  • Legacy Dialogs

  • Scatter/Dot...


A window pops up

A Window pops up

Select simple

Choose Define


Adding case labels

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

Including a fit Line with your Scatterplot


Correlations

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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