1. PS 225 Lecture 21 Relationships between 3 or More Variables

2. Relationships Between Multiple Variables  Three or more variables can be interrelated  Confounding variables  Example: Individuals given the medication Lipitor are more likely to die of a heart attack

3. Partial Correlation  Changes in a bivariate relationship when a third variable is introduced  Third variable (z) is a control variable

4. Variable Types  X Interval-ratio Independent  Y Interval-ratio Dependent  Z Any level of measurement Control

5. Correlation Coefficient  R xy  R xz  R zy  Detailed notation for R  Relationship between 2 variables without incorporating third variable  Zero-order correlation

6. Partial Correlation Coefficient  R xy,z  Detailed notation for R  Relationship between x and y controlling for z  First-order partials

7. Types of Relationships  Direct  Spurious  Intervening  Example: Possible relationship between geographic location, school performance and poverty

8. Direct Relationship X causes changes in Y. R xy and R xy,z are similar. X Y

9. Spurious Relationship Z has a relationship with both the independent and dependent variable. R xy and R xy,z are different Z X Y

10. Intervening Relationship Z has a relationship with both the independent and dependent variable. R xy and R xy,z are different. Z X Y

11. Determining Relationship 1. Establish existence of a relationship between independent (x) and Dependent (y) variables 2. Explore relationship between x, y and any associated confounding variables (z) 3. Calculate partial correlation coefficient and identify relationship type

12. Multiple Regression  Include any number of variable  Coefficients are partial slopes  Remove non-significant coefficients from the equation

13. SPSS Assignment Last class we answered the following questions: Does the number of years of education an individual has affect the hours of television a person watches? Does age affect the hours of television a person watches? This class: Use SPSS to find the regression equation that best represents the relationship between age and hours of television a person watches. Treat years of education as a confounding variable. Give the relationship between each pair of variables. Calculate the partial correlation coefficient. What is the most probable relationship type between variables? Give the multiple regression equation and predict the number of hours of television you watch. Compare the prediction to the actual number of hours.