1. Correlations
FSE 200

2. What You Will Learn in Chapter 5
All about correlation coefficients…
What they are
How to compute them
How to interpret them
Using the CORREL function
Data Analysis Toolpak
Other types of correlations and when to use them

3. What Correlations Are About…
Examines the relationship between variables
How the value of one variable changes in relation to changes in another variable
Range between -1 and 1
Bivariate correlation (2 variables)
Pearson product-moment correlation
Karl Pearson

4. Types of Correlation Coefficients
Positive correlation
Direction correlation
When variables change in the same direction
Negative correlation
Indirect correlation
When variables change in opposite directions
rXY = correlation between X and Y

5. Relationships Between Variables
Types of Correlations and Relationships

6. Computing Simple Correlations
Pearson product-moment…
What do these symbols represent?

7. Steps in Computation List the two values for each participant
Compute the sum of X values, and compute the sum of Y values
Square the X values, and
square the Y values
Find the sum of the XY products
Now plug these values into the formula

8. CORREL Function
Data for computing the correlation coefficient

9. CORREL Function
Computing the correlation coefficient

10. Scatterplot
A simple scatterplot

11. Scatterplot
A perfect direct or positive correlation

12. Strong Positive Relationship
A strong positive correlation

13. Strong Negative Relationship
A strong indirect relationship

14. Correlation Matrix Income Education Attitude Vote 1.00 0.35 -0.19 0.51
-0.21
0.43
0.55

15. Data Analysis Toolpak
The correlation dialog box

16. Data Analysis Toolpak
Entering the input range information

17. Data Analysis Toolpak
A correlation matrix

18. Interpreting Correlation Coefficients
Size of the Correlation Coefficient Interpretation
.8 to 1.0 Very strong relationship
.6 to .8 Strong relationship
.4 to .6 Moderate relationship
.2 to .4 Weak relationship
.0 to .2 Weak or no relationship

19. Variance Explained Coefficient of determination
rxy = .70
.702 = .49 or 49%
Coefficient of alienation
.702 = .49
1.00 – .49 = .51 or 51%

20. How Variables Share Variance
Remember: Association, not Causation

21. Types of Correlations

22. Summary
Showing how things are related to one another and what they have in common is a powerful idea and a very useful descriptive statistic. Correlations express a relationship that is only associative.
This statistic gives us valuable information about relationships and how variables change or remain the same.

23. Acknowledgement
The majority of the content of these slides were from the Sage Instructor Resources Website