1. Chapter 8: Relationships among Variables
SFM 651:
Research Methods
Dr. Johnson

2. Correlation
A statistical technique used to determine the relationship between 2 or more variables.
Positive – Small –> Small or Large -> Large
Ex……Strength and body weight
Negative – Small -> Large or Large -> Small
Ex……Driving distance vs driving accuracy
No relationship – it is more random

3. Correlation Correlation does not imply cause and effect
Necessary, but not sufficient

4. Pearson Product Moment coefficient of correlation
Most commonly used method of computing correlation r
There is a line of best fit.

5. What does r mean?
Significance – reliability or confidence in the likelihood of a statistic occurring again if the study were repeated.
Coefficient of determination = r²
Used to interpret meaningfulness of correlation
How much is related to the other = listed as a %

6. Predictions Line of best fit.
Is there a line that most closely fits inside the data?
Can be positive or negative

7. Partial and semi partial correlations
A 3rd variable has an effect
Shoe size and math score (age?)
Semipartial
One variable is taken out from other two

8. Multiple Regressions
Model used for predicting a criterion from 2 or more independent variable
Golf score
Driving distance
Driving accuracy
Greens in regulation
Scrambling
Putting

9. Multiple Regressions
Y= A+ (b1X1)+(b2X2)+ …… + (biXi)

10. Problems with Multiple Regressions
Shrinkage –
Validity decreases when prediction formula is used with a new sample
Population Specificity
Regression equation loses accuracy when put into a new sample.

11. Factor analysis
Used to reduce a set of data by grouping similar variables