1. Ch. 11: Quantifying and Interpreting Relationships Among Variables

2. Correlation Coefficient
A single number indicating the strength of association between 2 variables.
To what extent does the association resemble a straight line?
Pearson r as coefficient of choice
Value ranges from 0 (no relationship) to 1 (perfect linear relationship)
Sign indicates direction of relationship

3. Correlation and Causation
Causation implies correlation, but correlation does not imply causation.
Temporal precedence problem
Third variable problem

4. Types of Variables Continuous variables Discrete variables
Dichotomous variables

5. Example of a Scatter Plot
This person scores a 10 on Exam 1 and a 40 on Exam 2

6. Scatter Plots of Different Values of the Correlation Coefficient

7. Pearson r
Assesses the linear relationship between two continuous variables
Product Moment Correlation
Conceptual Formula:

8. Alternative Formula for Pearson r

9. Spearman Rho
Assesses the linear relationship between two variables that are in the form of ranked data
Formula:
“D” is the difference between the pairs of ranked scores
“6” is a constant
“N” is the number of score pairs

10. Point-Biserial Correlation
One variable is continuous and the other is dichotomous
Dummy coding is used to quantify the one dichotomous variable
Formula is same as Pearson r

11. Phi Coefficient Both variables are dichotomous
Could convert scores to z-scores and use Pearson r formula

12. Alternative Formula for Phi
“2 X 2 Table of Frequencies (or Counts)” A D C B