Chapter 10 CORRELATION Correlation Coefficient o Type of

Chapter 10 CORRELATION

Correlation Coefficient o Type of Data Required

Correlation Coefficient o Pearson’s r n n Strength of relationship Direction of relationship

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

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

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

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

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

Correlation Coefficient o Values of +1. 00 to -1. 00

Values of r o. 00 -. 25 Very Low o. 26 -. 49 Low o. 50 -. 69 Moderate o. 70 -. 89 High o. 90 - 1. 00 Very High

CORRELATION COEFFICIENT o Meaningfulness n n r squared shared variance

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

SPSS - Correlation o ANALYZE n Correlate p Bivariate o GRAPHS n Scatter

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

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

Phi o Both variables are dichotomous o Generally used with chi-square

Point-Biserial o One dichotomous variable o One continuous variable

Spearman Rho o Two ranked variables

Nonparametric Measures of Relationship o Kendall’s Tau o Contingency Coefficient

Kendall’s Tau o Two ordinal variables

Contingency Coefficient o Two nominal level variables o Associated with chi-square

Estimates of r o Biserial o Tetrachoric

Biserial o One dichotomized variable o One continuous variable

Tetrachoric o Two dichotomized variables

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

Partial Correlation o Method of control o Measures the correlation between two variables after removing the effect of another variable on both of the variables being correlated o r 12. 3

Semi-Partial Correlation o Measure of control o Measures the correlation between two variables after the effect of another variable has been removed from one of the variables being correlated o r 1(2. 3)

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

Example from the Literature