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4.15 Three Factor Factorial Designs complete interaction model

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 yi y k +y ( )jk=y jk y j y k +y

Three-Factor Factorial Designs: Fixed Factors A, B, C 175 Three Factor Factorial Example In a paper production process, the e ects of percentage of hardwood concentration in raw wood pulp, the vat pressure, and the cooking time on the paper strength were studied. There were a= 3 levels of hardwood concentration (CONC = 2%, 4%, 8%).

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