# lect16 - IE 410 Design of Experiments Lecture 16 Factorial...

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IE 410 Design of Experiments Lecture 16 Factorial Designs Continued

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Sample Size: Both factors fixed. The basic procedure is the same: Specify a practically significant difference you want to detect: Or equivalently, define how false H 0 should be for you to detect with probability beta.
However, here we are testing 3 separate H 0 's Solution: you could calculate n for each H 0 , and pick the biggest. Other than that, the procedure is basically the same.

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For factor A hypothesis: Φ 2 = nbD 2 /2a σ 2 v 1 = a-1 v 2 = ab(n-1) For factor B hypothesis: Φ 2 = naD 2 /2b σ 2 v 1 = b-1 v 2 = ab(n-1)
For the interaction hypothesis: Φ 2 = n D 2 /2[(a-1)(b-1)+1] σ 2 v 1 = (a-1)(b-1) v 2 = ab(n-1)

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Example: a=3 b=3 guess σ = 25 Test H 0 : T(i)'s = 0 at α =0.05 If any pair of means differ by D=40, then we should detect with probability = power =1- β = 0.95
Φ = SQRT(n*3*40*40/2*3*25*25) = SQRT(1.28*n) n Φ v 1 v 2 β ----------------------------- 2 1.6 2 9 0.5 3 1.96 2 18 0.18 4 2.26 2 27 0.06 5 2.53 2 36 0.03

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lect16 - IE 410 Design of Experiments Lecture 16 Factorial...

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