1. Psychology 202a Advanced Psychological Statistics
November 7, 2017

2. The Plan for Today
ANOVA: the traditional approach
ANOVA in SAS

3. 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

4. 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
Analogue of the pooled variance estimate
Variance estimate based on the Central Limit Theorem

5. Analogue 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:

6. Variance estimate based on the Central Limit Theorem
The CLT says that
If we substitute sample estimates and do a little algebra, this becomes

7. Variance estimate based on the Central Limit Theorem
That idea leads to

8. Illustration with example
Massed practice:
mean = , variance =
Spaced practice:
mean = , variance =
No practice:
Mean = , variance =
In each case, n = 8.

9. Organizing the information
Source SS df MS F
Between 2
5.85
Within 21
Total 23

10. 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.

11. Practical ANOVA ANOVA in SAS ANOVA in R Assessing the assumptions in R
Visualizing ANOVA in R

12. Next time
ANOVA as a special case of regression