Transcription of 4.15 Three Factor Factorial Designs complete interaction model
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Factor Factorial Designs Thecomplete interaction modelfor a Three - Factor completely randomized design is:yijkl=(35) is the baseline mean, i, j, and kare the main Factor effects forA,B, andC, respectively. ( )ij, ( )ikand ( )jkare the two- Factor interaction effects for interactionsAB,AC, andBC, respectively. ( )ijkare the Three - Factor interaction effects for theABCinteraction. eijklis the random error of thekthobservation from the (i,j,k) assumeeijkl IID N(0, 2). For now, we will also assume all effects are Partitioning the total sum of squares SST= ai=1 bj=1 ck=1 nl=1(yijkl y )2 Note that we can rewriteyijklasyijkl= + i+ j+ k+ ( )ij+ ( )ik+ ( )jk+ ( )ijk+eijklwhere =y i=yi y j=y j y k=y k y ( )ij=yij yi y j +y ( )ik=yi k
To understand the e ects in the model, we need to examine the interaction plots. THREE FACTOR ANALYSIS OF VARIANCE The GLM Procedure Dependent Variable: strength Source DF Sum of ... 2 400 2 500 2 650 4 400 4 500 4 650 8 400 8 500 8 650 conc*press D istribution of strength strength Level of conc Level of press N Mean Std Dev
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