yates - where X12 = X1 column * X2 column = (+1, -1, -1,...

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Yates Algorithm and Estimating Factor Effects in Design of Experiment Design Observations (divide #2 with Replicates Data Yates Algorithm by #runs) Run x1 x2 R1 R2 R3 R4 Average #1 #2 Estimate Effect 1 - 1 - 1 y11 y12 y13 y14 y1 y1 + y2 (y1 + y2) + (y3 + y4) See “Mean” Average 2 +1 - 1 y21 y22 y23 y2 y3 + y4 (y2 - y1) + (y4 - y3) See “F1” Effect X1 3 - 1 +1 y31 y32 y3 y2 - y1 (y3 + y4) - (y1 + y2) See “F2” Effect X2 4 +1 +1 y41 y42 y43 y44 y4 y4 - y3 (y4 - y3) - (y2 - y1) See “F12” Effect X12 “Mean” = [ (y1 + y2) + (y3 + y4) ] / 4 = (y1 + y2 + y3 + y4) / 4. Effect X1 is estimated by “F1” = [ (y2 - y1) + (y4 - y3) ] / 4 = [ (y2 + y4)/2 - (y1 + y3)/2 ] / 2 = ( - y1 + y2 - y3 + y4) / 4 (see the design layout for factor X1) Estimate of Effect X2 is “F2” = [ (y3 + y4) - (y1 + y2) ] / 4 = [ (y3 + y4)/2 - (y1 + y2)/2 ] / 2 = ( - y1 - y2 + y3 + y4) / 4 (see the design layout for factor X2) Estimate of Effect X12 (Interaction) is “F12” = [ (y4 - y3) - (y2 - y1) ] / 4 = [ (y4 - y3)/2 - (y2 - y1)/2 ] / 2 = (y1 - y2 - y3 + y4) / 4 (see the design layout for factor X12 given below),
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Unformatted text preview: where X12 = X1 column * X2 column = (+1, -1, -1, +1). Exercise 1: Check if the calculation of the 2^2 experiment (with two replicates in each run) given in the 08/22/02 lecture is correct. Exercise 2: Estimates the average, main effects X1, X2, X3, two-factor interactions X12, X13, X23, three-factor interaction X123 by using Yates Algorithm explained above. Design Observations (divide #2 with Replicates Data Yates Algorithm by #runs) Run x1 x2 X3 R1 R2 R3 R4 Average #1 #2 #3 Estimate Effect 1-1-1-1 y11 y12 y13 y14 y1 = 79.7 Average 2 +1-1-1 y21 y22 y23 y2 = 74.3 Effect X1 3-1 +1-1 y31 y32 y3 = 76.7 Effect X2 4 +1 +1-1 y41 y42 y43 y44 y4 = 70.0 Effect X12 5-1-1 +1 y51 y52 y5 = 84.0 Effect X 3 6 +1-1 +1 y61 y62 y63 y6 = 81.3 Effect X1 3 7-1 +1 +1 y71 y72 y7 = 87.3 Effect X2 3 8 +1 +1 +1 y81 y82 y83 y8 = 73.7 Effect X12 3 Exercise 3: See handout for another example with 2^4 ( = 16 runs)....
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yates - where X12 = X1 column * X2 column = (+1, -1, -1,...

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