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 ) 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 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.

MEASURES OF ASSOCIATION

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)

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.

Measures of association For Cross-Tabs Nominal Strength Significance Ordinal Strength Significance Direction!

Ordinal Measures of Association MeasureRangeCharacteristics Gamma-1.0 to 1.0Tends to be generous Kendall's Tau B-1.0 to 1.0For square tables Kendall's Tau C-1.0 to 1.0For rectangular Somers’ D-1.0 to 1.0Our preferred measure

HOW TO CONTROL FOR A VARIABLE? Adding 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 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 Pearson’s Product Movement (Pearson’s r) A way of measuring the goodness of fit between two continuous variables Note the lower case r

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.v by knowing the independent variable. We call this a r 2 (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- – weak-moderate – moderate – 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

SCATTERPLOTS

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)