STAT 4220 HW6

STAT 4220 HW6 - n th number of replication, and i,j,k are...

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Austin Wen HW #6 STAT 4220 1. 9 x 9 Latin Square Design A B C D E F G H I H D F G C I E B A I G E B H A C F D D C H F A E B I G G E B H I D F A C F I A C B G H D E B H G I D C A E F C A D E F H I G B E F I A G B D C H 2. a. = - - - + dFresidual IJKn I J K 2 , where n is number of replicates. b. ={ = = = = - ...- . ..- . . ..+ …. } - - - + σ2 i 1Ij 1Jk 1Kl 1nyijkl yi y j y k 2y 2 IJKn I J K 2 c. ( ) = ..- …- . ..+ …. αβ ij yij yi y j y d. ( ) = . .- …- . . .+ …. αγ ik yi k yi y k y e. ( ) = . .- . ..- . . .+ …. βγ jk y jk y j y k y f. g. =( , , )∈ - ...- . ..- . . ..+ …. - ( - ) σ2 i j k Syijkl yi y j y k 2y 2K 1 K 2 In Latin Square Design, the estimate σ2 is similar to the three-way layout model’s expression except there is no
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Unformatted text preview: n th number of replication, and i,j,k are specifically assigned to specific cell instead of running from 1 to I,J,or K. h. i. Time and resources are the two big reasons. If we conduct the 5 x 5 x5 three-way layout experiment, we will have to collect total 125 sample data. However, we can use the Latin Square Design with only 25 sample data from the experiment that still can give a meaningful conclusion. j....
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