1. Introduction to Behavioral Statistics
Correlation & Regression

2. Correlation Introduction to Correlation & Regression
We often see things that are related to one another.
height/weight
IQ/Performance in School
Age/Income
We call this relationship Correlation
Pearson r is the most common method of measuring relationship. W

3. Correlation Formula for calculating Pearson’s r
Let x and y be two sets of paired observations with standard deviations = sx and sy
How might we measure relationship between two sets of scores?

4. Correlation
How might we measure relationship between two sets of scores?

5. Correlation Is this a good measure of relationship?
It does give different values for different degrees of relationship.
It does not provide consistency which allows it to be interpreted.
Every set of scores will yield a different score
The result will vary with the size of the scores.
How can we equalize these scores so they will give consistent and meaningful results every time?

6. Correlation
How can we equalize these scores so they will give consistent and meaningful results every time?
We can change the scores to standard scores and take the average product of the standard scores for the X and Y variables.

7. Correlation

8. Correlation This is called the standard score formula.
It is a defining formula
It is not a formula that you would use to actually calculate the correlation coefficient.
We call this the Pearson Product Moment r

9. Pearson Product Moment Correlation Coefficient
The most widely used method of measuring correlation is the Pearson Product Moment Correlation.
We will also consider a Rank Order Correlation Coefficient
It is an Ordinal Level Correlation Method
Spearman Rank Order Correlation
Limits for Correlation are

10. Pearson Product Moment Correlation Coefficient
Calculating Pearson’s Product Moment r

11. Pearson Product Moment Correlation Coefficient
Example Illustrating Computation of Pearson’s r

12. Pearson Product Moment Correlation Coefficient
Calculating Pearson’s Product Moment r

13. Pearson Product Moment r

14. Pearson Product Moment r
Computation of r from raw scores

15. Pearson Product Moment r
Computation of r from raw scores

16. Spearman Rank Difference Correlation (Rho)(D)
We sometimes have data we want to correlate which doesn’t meet the requirements for a Pearson r.
Not at Interval Level
Rho is a correlation technique that requires only ordinal level of measurement.

17. Spearman Rank Difference Correlation (Rho)(D)

18. Spearman Rank Difference Correlation (Rho)
Advantages and Disadvantages of Rho
Advantages:
Ease of Computation
Skewness influences r but not Rho
Disadvantages:
It is somewhat less consistent from sample to sample.

19. Spearman Rank Difference Correlation (Rho)
Next We will focus on interpreting a correlation coefficient and regression.
Press Here to Return to CLASS PAGE