Transcript Political Research and Statistics

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
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
Association
Range
Lambda
0 - 1.0
Phi
0 - 1.0
Cramer's V
0 - 1.0
Characteristics
may underestimate, but a
PRE measure
Use for a 2x2 table only and
is Chi-square based
Chi-square based and the
compliment to PHI.
Measures of association For Cross-Tabs
Nominal
• Strength
Ordinal
• Strength
• Significance
• Significance
• Direction!
Ordinal Measures of Association
Measure
Range
Characteristics
Gamma
-1.0 to 1.0
Tends to be generous
Kendall's Tau B
-1.0 to 1.0
For square tables
Kendall's Tau C
-1.0 to 1.0
For rectangular
Somers’ D
-1.0 to 1.0
Our preferred measure
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.v by
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
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...
Select simple
Choose Define
A Window pops up
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)