1. Chapter 10
CORRELATION

2. Correlation Coefficient
Type of Data Required

3. Correlation Coefficient
Pearson’s r
Strength of relationship
Direction of relationship

4. Correlation Coefficient
Assumptions
Sample must be representative of the population
Variables being correlated must each have a normal distribution
Homoscedasticity
Linear relationship

5. CORRELATION Power Analysis .10 = small effect .30 = moderate effect
.50 = large effect

6. Correlation Power Analysis Two-tailed test Alpha = .05
Moderate effect = .30
Power = .80
Sample size = 84

7. Correlation Power Analysis One-tailed Alpha = .05
Moderate effect = .30
Power = .80
Sample size = 68 subjects

8. CORRELATION Power Analysis Small sample = 20 subjects Alpha = .05
Moderate effect = .30
Power = .25

9. Correlation Coefficient
Values of to -1.00

10. Values of r .00 - .25 Very Low .26 - .49 Low .50 - .69 Moderate
High
Very High

11. CORRELATION COEFFICIENT
Meaningfulness
r squared
shared variance

12. Computer Example
What are the correlations between the following variables?
Confidence
Life Satisfaction
Total IPPA Score

13. SPSS - Correlation
ANALYZE
Correlate
Bivariate
GRAPHS
Scatter

14. Confidence Intervals 1. Transform r to Zr, using Appendix D
2. Calculate standard error
3. Decide on level of confidence
4. Transform intervals back to zrs, using Appendix D

15. Shortcut Versions of r
1. Phi
2. Point-Biserial
3. Spearman Rho

16. Phi
Both variables are dichotomous
Generally used with chi-square

17. Point-Biserial
One dichotomous variable
One continuous variable

18. Spearman Rho
Two ranked variables

19. Nonparametric Measures of Relationship
Kendall’s Tau
Contingency Coefficient

20. Kendall’s Tau
Two ordinal variables

21. Contingency Coefficient
Two nominal level variables
Associated with chi-square

22. Estimates of r
Biserial
Tetrachoric

23. Biserial
One dichotomized variable
One continuous variable

24. Tetrachoric
Two dichotomized variables

25. “Universal” Measure of Relationship
Eta or Correlation ratio
Used to measure nonlinear, as well as linear relationship
Values go from 0 to 1

26. Partial Correlation Method of control
Measures the correlation between two variables after removing the effect of another variable on both of the variables being correlated
r12.3

27. Semi-Partial Correlation
Measure of control
Measures the correlation between two variables after the effect of another variable has been removed from one of the variables being correlated
r1(2.3)

28. Multiple Correlation
The correlation of a group of independent variables with one dependent variable
Measures the correlation between the dependent variable and a weighted composite of the independent variables
R is the symbol
R squared is used to define the variance accounted for in the dependent variable

29. Example from the Literature