1. Psychology 202b Advanced Psychological Statistics, II March 3, 2011

2. Overview Wrapping up mixed categorical and continuous predictors. Power analysis for regression.

3. Mixing categorical and continuous predictors Example: BMI predicted by Father’s occupation and family income. –Interpretation as separate regression for each occupation group. –Testing the collective need for the interactions.

4. Power analysis for regression Review of the concept of statistical power. –Type I and Type II errors. –Noncentral distributions and noncentrality parameters. Statistical power and regression. –Power analysis focused on R 2. –Power analysis focused on  R 2. –Power analysis for a particular slope.

5. Power analysis focused on R 2 Effect size: Noncentrality parameter: Illustration in R. Illustration in Gpower.

6. Power analysis focused on  R 2 Effect size: Noncentrality parameter: Illustration in R. Illustration in Gpower.

7. Power analysis for a particular slope Change the question into power analysis for  R 2. The slope is related to the semi-partial correlation: Hence

8. Power analysis for a particular slope That implies that an assumption must be made about how much X overlaps with the other predictors. An upper bound for power can be obtained by assuming that X is independent of the other predictors. Illustration in R. Illustration in Gpower.

9. Next time Continuous interactions.