1. Lecture 5 zToday: More Sections 2.1-2.3 zPlease read these sections. You are responsible for all material in these sections…even those not discussed in class zAssignment #1: Due on Thursday zAssignment #2: Chapter 2: 6…more to come

2. Two-Way ANOVA zOne-way ANOVA considered impact of 1 factor with k levels (e.g. battery example) zTwo-way ANOVA considers the impact of 2 factors with I and J levels respectively zHave possible treatments for each replicate of the experiment zIf have n replicates, the the experiment has observations

3. Example: zAn experiment was run to understand the impact of two factors (Table speed and Wheel grit size) on the the strength of the ceramic material (bonded S i nitrate). (Jahanmir, 1996, NIST) zEach factor has two levels (coded -1 and +1 respectively) zThe experiment was repeated 2 times

4. Data

5. zModel:

6. Constraints zSum-to-zero: zBaseline:

7. Hypotheses

8. Running the Experiment zTwo-Way ANOVA Model is appropriate for experiments performed as completely randomized designs zThat is, we list the treatments (e.g., 1-8 in the ceramics example) and assign treatments to experiemntal units in random order. zThe trials are in random order

9. ANOVA Table

10. Return to Ceramic Data

11. Interaction Plot

12. ANOVA Table (S-Plus or R)

13. zWhat would happen if the experiment was unreplicated (l =1)? zWhat could we do to address this?

14. Multi-Way (or N-Way) ANOVA (Section 2.4) zCan extend model to more that 2 factors zApproach is the same

15. Experiment Situation zHave N factors zThe experiment is performed as a completely randomized design zAssumptions: