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Lecture3 - -3-4 A B AB(1 = 20 a = 40 b = 30 ab = 52...

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Introduction to Factorial Designs © Diane Schaub, University of Florida Lecture3.ppt

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Lecture3.ppt © Diane Schaub, University of Florida What are Factorial Designs? Used for simultaneous study of two or more factors. All possible combinations of the levels of the factors are investigated in each complete trial or replication of the experiment For example, if there are a levels of factor A, and b levels of factor B, each replicate contains all ab treatment combinations.
Lecture3.ppt © Diane Schaub, University of Florida Two-Factor Example Suppose we have a two-factor experiment with both design factors at two levels. Two levels are called “low” and “high” and denoted “ –” and “ +”, respectively - (Low) + (High) + (High) - (Low) Factor A Factor B 52 40 30 20 Figure 5-1, p. 161 [The response y is shown at the corners of the cube]

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Lecture3.ppt © Diane Schaub, University of Florida Calculating Average Response 40 52 20 30 21 2 2 30 52 20 40 11 2 2 A B + + = - = + + = - = Main Effects 1 - - + 2 + -

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Unformatted text preview: -3-+-4 + + + A B AB (1) = 20 a = 40 b = 30 ab = 52 Lecture3.ppt © Diane Schaub, University of Florida Factorial Plot Showing No Interaction Between Factors 10 20 30 40 50 60 Low High B-B+ Fig. 5-3 Factor A Response Lecture3.ppt © Diane Schaub, University of Florida Two-Factor Example (cont.) Now let’s assume that we have a two-factor example that contains an interaction -(Low) + (High) + (High)-(Low) Factor A Factor B 12 50 40 20 Figure 5-2, p. 161 [The response y is shown at the corners of the cube] Lecture3.ppt © Diane Schaub, University of Florida Calculating Average Response 50 12 20 40 1 2 2 40 12 20 50 9 2 2 A B + + =-= + + =-= -Main Effects 1--+ 2 +--3-+-4 + + + A B AB (1) = 20 a = 50 b = 40 ab = 12 Lecture3.ppt © Diane Schaub, University of Florida Factorial Plot Showing a Strong Interaction Between Factors 10 20 30 40 50 60 Low High B-B+ Fig. 5-4 Factor A Response...
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Lecture3 - -3-4 A B AB(1 = 20 a = 40 b = 30 ab = 52...

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