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.

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Presentation transcript:

Lecture 5 zToday: More Sections 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

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

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

Data

zModel:

Constraints zSum-to-zero: zBaseline:

Hypotheses

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

ANOVA Table

Return to Ceramic Data

Interaction Plot

ANOVA Table (S-Plus or R)

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

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

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