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lect15 - IE 410: Design of Experiments Lecture 15:...

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IE 410: Design of Experiments Lecture 15: Factorial Experiments Well we have been hinting at, and preparing for multi-factor experiments for a while, finally they are here.
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To start, assume two factors, A, and B. The results generalize pretty easily to more than 2 factors. Example : Y=Yield A=temp B=Pressure A at 2 levels, 20 degrees, 30 degrees B at two levels 1 atms. , 2 atms.
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A Simple Factorial Experiment: Pressure 1 2 ------------------ 20 | 15,25 | 27, 23 | Temp |-------|--------| 30 | 36,44 | 49, 55 | ------------------
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Note: a=2, b=2, n=2
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A table of cell averages: Pressure 1 2 ------------------ 20 | 20 | 25 | Temp |-------|--------| 30 | 40 | 52 | ------------------
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Does temp have an effect?
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Define the "Factor A main effect" measures what happens as we go from A at one level to A at another level: The Factor A TOTAL Effect is: (40+52) - (20+25) = 47
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The Factor A average effect is: = Ave(30 degrees) - Ave(20 degrees) = (40+52)/2 - (20+25)/2 = 23.5 Note that both are contrasts
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B main effect Total effect = (25+52) - (20+40) = 17 Ave effect = (25+52)/2 - (20+40)/2 = 8.5
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Note that the grand total is: (20+40+25+52) = 137 And the Grand Average is: (20+40+25+52)/4 = 34.25
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Finally, the (total) interaction effect AB = (20+52) - (40+25) = 7
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lect15 - IE 410: Design of Experiments Lecture 15:...

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