Class Meeting 27

Class Meeting 27 - CHEN 3010 Applied Data Analysis Class...

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CHEN 3010 Applied Data Analysis Class Meeting #27 Tuesday, Dec. 7th Today's Topics Homework #11 due: Wednesday 12 noon! (per your request) Thursday’s class: Review, Past tests, FCQ Finals on Friday December 10 th , 1:30 pm – 4 pm Experimental Design 2 k Design for k > 2 Blocking & Confounding Fractional Factorial Design
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3-factor, 2-level Factorial Design – 2 3 A B C +1 +1 +1 -1 -1 -1 (1) a b c ab ac bc abc Main effect for A average at A=+1 average at A=+1 - A = ( ) 1 b c bc a ab ac abc A 44 +++ = with n replicates ( ) 1 b c bc a ab ac abc A 4n = ⋅⋅ In terms of A contrast ( ) ( ) 1 A 1 a b ab c ac bc abc = + −+ + Similar main effects for B and C
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Two-way Interactions AB Interaction ( ) ( ) ( ) ( ) ( ) ac a c 1 ab abc b bc 1 n2 2 AB 2  + −+ +   = AB = A effect at B=+1 A effect at B=-1 - 2 A B C +1 +1 +1 -1 -1 -1 (1) a b c ab ac bc abc - + In terms of AB contrast ( ) 1 AB 1 a b ab c ac bc abc 4n = −−+ +−
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3-way Interaction ABC average difference of AB interactions for two levels of C ( ) 1 ABC 1 a b ab c ac bc abc 4n = + +− +   Treatment I A B C AB AC BC ABC (1) 1 -1 -1 -1 1 1 1 -1 a 1 1 -1 -1 -1 -1 1 1 b 1 -1 1 -1 -1 1 -1 1 ab 1 1 1 -1 1 -1 -1 -1 c 1 -1 -1 1 1 -1 -1 1 ac 1 1 -1 1 -1 1 -1 -1 bc 1 -1 1 1 -1 -1 1 -1 abc 1 1 1 1 1 1 1 1 Effect Factorial Design Layout Table ABC contrast dot-product of these columns gives ABC contrast
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General Formulae for Effect, Variance, & s.e. [ ] k1 Contrast Effect n2 = where the contrast can be easily computed from the dot-product Text presents analysis of experimental results based on confidence intervals (see Example 7-1, Table 7-6, page 327) Additional results, analysis of variance (ANOVA),are shown in Minitab output, to test the significance of interactions.
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Class Meeting 27 - CHEN 3010 Applied Data Analysis Class...

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