Transcript Correlation - Southeast Missouri State University

Correlation
CJ 526 Statistical Analysis in
Criminal Justice
Introduction
1. Correlation:
Correlation and Prediction
1. If a relationship exists between two
variables
Correlation and Ex Post Facto
Designs
1. Usually used with ex post facto designs
1. No manipulation of independent variable by the
researcher
Requirements for Correlation
1. Requires two scores for each unit of
analysis:
1. X
2. Y
Scatterplot
1. Graphical representation of relationship
between the two variables
GPA
ACT
Characteristics of a Relationship
1. Direction (sign)
1. +: Positive
2. -: Negative
Direction
1. Positive
As one variable increases, the other increases
Scatterplot goes to the right
Direction -- continued
2. Negative
As one variable increases, the other
decreases
Scatterplot goes to the left
Magnitude
1. Strength
Magnitude -- continued
6. Closer to 1, stronger the relationship
1. Less predictive error
Magnitude -- continued
8. Zero correlation
1. Result of no systematic relationship between X
and Y
2. Knowing X would be of no value in predicting Y
Magnitude -- continued
10. Perfect correlations can be positive or
negative
Interpretation Heuristic for
Magnitude: Positive Correlation
Correlation
Coefficient Range
0 to 0.4
0 to -.4
0.4 to 0.8
-.4 to -.8
0.8 to 1.0
-.8 to -1.0
Description
No to weak relationship
Moderate relationship
Strong relationship
Form
1. Form:
Linear and non-linear relationships
Linear Relationship
1. Linear relationship
1. Every change in X is accompanied by a
corresponding change in Y
Nonlinear Relationship
1. No linear relationship
1. A change in X does not correspond to any
predictable change in Y
Example: 0 correlation
Parabola
Nonlinear Relationships
1. Exponential
1. Time and retention
Retention
Time
Performance
Arousal
Use of Correlation
1. Reliability
Test-retest and split-half
Pearson Product-Moment
Correlation
1. Measures the direction and strength of
the linear relationship between two
variables
Pearson Product-Moment
Correlation -- continued
3. degree to which X and Y vary together
(covariance)
1. divided by
Correlation and Causality
1. Correlation does not imply causality
Criteria for Causality
1. Relationship between X (presumed
cause) and Y (effect)
Poverty and Crime
1. Poverty and crime are related
Factors Affecting Pearson
Correlation
1. Restricted range
1. Could overestimate or underestimate
Interpreting Correlation in Terms
of Variance
1. Coefficient of Determination
1. Proportion of variance of Y that is explained or
accounted for by the variance of X
R squared
Coefficient of Nondetermination
1. Proportion of variance of Y that is not
explained or accounted for by the
variance of X
r
0.0
.2
.4
.6
.8
.9
r2
0.0
.04
.16
.36
.64
.81
%
Explained
0
4
16
36
64
81
1 - r2
1.0
.96
.84
.64
.36
.19
%
Unexplained
100
96
84
64
36
19
SPSS Procedure Graphs
• Use to generate scatterplot
– Determine whether the relationship is linear
• Graphs, Scatter
– Simple
• Define
SPSS Procedure Correlate
• Analyze, Correlate, Bivariate
– Move variables over
– Options
• Statistics
– Means and standard deviations
SPSS Procedure Correlate
Output
• Descriptive Statistics
–
–
–
–
Variables
Mean
Standard Deviation
N
• Correlations
– Pearson Correlation
– Sig (2-tailed)
– N
Hypothesis Tests With Pearson
Correlations
•
•
•
•
H0: The population correlation is zero
H1: The population correlation is non-zero
 (rho)
df = N - 2
Report Writing
• A correlation for the data revealed that
population and crime rate were
significantly related, r = .97, n = 32, p <
.01, two tails.