Transcript 11/17/2015
Psychology 202a Advanced Psychological Statistics November 17, 2015 The Plan for Today • ANOVA: the traditional approach (continued) • ANOVA in SAS • ANOVA assumptions • Visualizing ANOVA • ANOVA as a special case of regression 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 Variance estimate based on the Central Limit Theorem • The CLT says that 2 σM = σ 2 n . • If we substitute sample estimates and do a little algebra, this becomes s = n sM . 2 2 Variance estimate based on the Central Limit Theorem • That idea leads to k MS M MS B n i 1 M i M k 1 2 . Illustration with example • Massed practice: – mean = 55.125, variance = 925.839286 • Spaced practice: – mean = 94.000, variance = 936.857143 • No practice: – Mean = 112.625, variance = 1668.26786 • In each case, n = 8. Organizing the information Source SS Between 13771.75 df MS F 2 6885.875 5.85 1176.988 Within 24716.75 21 Total 38488.5 23 Assumptions of the ANOVA • • • • • Independence between groups Independence within groups Homoscedastic populations Normal populations In other words, the assumptions are identical to those of the t test, generalized to more than two groups. Practical ANOVA • ANOVA in SAS • Assessing the assumptions in R • Visualizing ANOVA in R