Transcription of 4.15 Three Factor Factorial Designs complete interaction …
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4.15 Three Factor Factorial Designs complete interaction …
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 ( )ijk=yijk yij yi k y jk +yi +y j +y k y eijkl=yijkl yijk Substitution of these estimates intoSSTyieldsSST=a i=1b j=1c k=1n l=1(yijkl y )2=a i=1b j=1c k=1n l=1( i+ j+ k+ ())
The complete interaction model for a three-factor completely randomized design is: y ijkl = (35) { is the baseline mean, { ˝ i, j, and k are the main factor e ects for A, B, and C, respectively. { (˝ ) ij, (˝) ik and ( ) jk are the two-factor interaction e ects for interactions AB, AC, and BC, respectively. { (˝ ) ijk are the three-factor ...
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