1. CJ 526 Statistical Analysis in Criminal Justice
Correlation
CJ 526 Statistical Analysis in Criminal Justice

2. Introduction
Correlation:

3. Correlation and Prediction
If a relationship exists between two variables

4. Correlation and Ex Post Facto Designs
Usually used with ex post facto designs
No manipulation of independent variable by the researcher

5. Requirements for Correlation
Requires two scores for each unit of analysis: X Y

6. Scatterplot
Graphical representation of relationship between the two variables

7. GPA
ACT

8. Characteristics of a Relationship
Direction (sign)
+: Positive
-: Negative

9. Direction Positive As one variable increases, the other increases
Scatterplot goes to the right

10. Direction -- continued
Negative
As one variable increases, the other decreases
Scatterplot goes to the left

11. Magnitude
Strength

12. Magnitude -- continued
Closer to 1, stronger the relationship
Less predictive error

13. Magnitude -- continued
Zero correlation
Result of no systematic relationship between X and Y
Knowing X would be of no value in predicting Y

14. Magnitude -- continued
Perfect correlations can be positive or negative

15. Interpretation Heuristic for Magnitude: Positive Correlation
Correlation Coefficient Range
Description
0 to 0.4
0 to -.4
No to weak relationship
0.4 to 0.8
-.4 to -.8
Moderate relationship
0.8 to 1.0
-.8 to -1.0
Strong relationship

16. Form
Form:
Linear and non-linear relationships

17. Linear Relationship Linear relationship
Every change in X is accompanied by a corresponding change in Y

18. Nonlinear Relationship
No linear relationship
A change in X does not correspond to any predictable change in Y
Example: 0 correlation
Parabola

19. Nonlinear Relationships
Exponential
Time and retention

20. Retention
Time

21. Performance
Arousal

22. Use of Correlation
Reliability
Test-retest and split-half

23. Pearson Product-Moment Correlation
Measures the direction and strength of the linear relationship between two variables

24. Pearson Product-Moment Correlation -- continued
degree to which X and Y vary together (covariance)
divided by

25. Correlation and Causality
Correlation does not imply causality

26. Criteria for Causality
Relationship between X (presumed cause) and Y (effect)

27. Poverty and Crime
Poverty and crime are related

28. Factors Affecting Pearson Correlation
Restricted range
Could overestimate or underestimate

29. Interpreting Correlation in Terms of Variance
Coefficient of Determination
Proportion of variance of Y that is explained or accounted for by the variance of X
R squared

30. Coefficient of Nondetermination
Proportion of variance of Y that is not explained or accounted for by the variance of X

32. SPSS Procedure Graphs Use to generate scatterplot Graphs, Scatter
Determine whether the relationship is linear
Graphs, Scatter
Simple
Define

33. SPSS Procedure Correlate
Analyze, Correlate, Bivariate
Move variables over
Options
Statistics
Means and standard deviations

34. SPSS Procedure Correlate Output
Descriptive Statistics
Variables
Mean
Standard Deviation N
Correlations
Pearson Correlation
Sig (2-tailed)

35. Hypothesis Tests With Pearson Correlations
H0: The population correlation is zero
H1: The population correlation is non-zero
 (rho)
df = N - 2

36. Report Writing
A correlation for the data revealed that population and crime rate were significantly related, r = .97, n = 32, p < .01, two tails.