PROC ANOVA is used to perform analysis of variance on experimental data. It allows specification of classification variables using CLASS, dependent variables using MODEL, and post hoc comparisons using MEANS. Examples show using PROC ANOVA to analyze a one-way ANOVA model with multiple comparisons, and a repeated measures ANOVA to analyze how an interest level changes over time. Questions ask about the differences between ANOVA and linear regression, the expected value of mean squared error, and fixed/random effects.

1. SAS tutorial: ANOVA

2. 作業(目前)沒有但考試會考的東西
• Full model/reduced model comparison
• Multiple comparison
• Post hoc analysis (regression)

3. PROC ANOVA
• CLASS
– Names the classification variables to be used in the model.
• MODEL
– dependents=effects </ options>
• TEST
– TEST <H= effects> E= effect
• MEANS
– MEANS effects </ options>
– Post hoc analysis for the effects specified.
• REPEATED; ABSORB; BY; FREQ; MANOVA

4. Example

5. Data
Y X1 X2 X3

6. SAS code
• proc anova data=cream;
• class batch position starter;
• model acidity=batch position starter;
• means batch starter /scheffe;
• run;

7. Result - Data

8. Result – Analysis of Variance

9. Result- Scheffe’s test (batch)

10. Result – Scheffe’s test (starter)

11. Example: Repeated measure
• 30 people
• Interest in voting (5-point scale)
• Measured in 10, 15, 20 years old

12. SAS code
data ex2; proc anova data=ex2;
do subject=1 to 30; class age subject;
do age=1 to 3; model interest=age subject
input interest @@; age*subject;
output; test h=age e=age*subject;
end; run;
end;
datalines;
1 1 3
1 1 3
...

13. Result - Data

14. Result - ANOVA

15. Result
test h=age e=age*subject;

16. Another way
• proc anova data=ex2;
• class age subject;
• model interest=age subject;
• run;

17. Result - ANOVA

18. Questions
• ANOVA跟linear regression的差別
• Mean squared error的期望值
• Fixed effect/random effect