1. Psychology 202a Advanced Psychological Statistics November 12, 2015

2. The Plan for Today Assumptions of multiple regression ANOVA: the traditional approach ANOVA in SAS

3. Assumptions for inference in multiple regression The relationships between predictors and the dependent variable must be linear. The errors must be independent. The errors must be homoscedastic. The errors must be normally distributed. In other words, the assumptions for multiple regression are the same as for simple regression.

4. ANOVA: the Traditional Approach A motivating example –Speed with which math problems are performed –Three practice conditions: massed, spaced, none The multiple testing problem A way out: –first, ask if any means differ –then worry about which means differ

5. How ANOVA works Logic: develop two ways of estimating variance: –one that always makes sense (given some assumptions) –one that depends on the null hypothesis Analog of the pooled variance estimate Variance estimate based on the Central Limit Theorem

6. Analog of the pooled variance estimate When we dealt with the t test, we pooled variance using a weighted average of the variance estimate in each group. This is easily modified to accommodate more than two groups: