Transcript 11/12/2015
Psychology 202a Advanced Psychological Statistics November 12, 2015 The Plan for Today • Assumptions of multiple regression • ANOVA: the traditional approach • ANOVA in SAS 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. 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 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 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: 2 n 1 s i i MS E MSW i 1k i 1n i 1 k