19SplitLME(1)

19SplitLME(1) - ANOVAANALYSISOFABALANCEDSPLIT-PLOT...

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Unformatted text preview: ANOVAANALYSISOFABALANCEDSPLIT-PLOT EXPERIMENT Example:thecorngenotypeandfertilizationresponsestudy Mainplots:genotypes,inblocks Splitplots:fertilization 2wayfactorialtreatmentstructure splitplotvariabilitynestedinmainplotvariabilitynestedinblocks. c 2011Dept.Statistics(IowaStateUniversity) Stat511section19 1/22 Field Block 1 Block 2 Block 3 Block 4 Genotype A Genotype B Genotype C Genotype A Genotype B Genotype C Genotype A Genotype B Genotype C Genotype A Genotype B Genotype C 50 100 150 50 100 150 150 100 50 150 100 50 100 50 150 100 50 150 100 150 50 50 100 150 50 100 150 150 50 100 150 100 50 50 150 100 Plot Split Plot or Sub Plot c 2011Dept.Statistics(IowaStateUniversity) Stat511section19 2/22 Amodel: y ijk = ij + b k + w ik + e ijk ij =MeanforGenotype i ,Fertilizer j Genotype i = 1 , 2 , 3 ,Fertilizer j = 1 , 2 , 3 , 4 ,Block k = 1 , 2 , 3 , 4 u = b 1 .. . b 4 w 11 w 21 .. . w 34 = b w N , 2 b I 2 w I u N , G 2 e I c 2011Dept.Statistics(IowaStateUniversity) Stat511section19 3/22 Source DF Blocks 4 1 = 3 Genotypes 3 1 = 2 Blocks Geno ( 4 1 )( 3 1 ) = 6 wholeplot u Fert 4 1 = 3 Geno Fert ( 3 1 )( 4 1 ) = 6 Block Fert ( 4 1 )( 4 1 ) + Blocks Geno Fert +( 4 1 )( 3 1 )( 4 1 ) 27 splitplot u C . Total 48 1 4 7 c 2011Dept.Statistics(IowaStateUniversity) Stat511section19 4/22 Source SumofSquares Blocks 3 i = 1 4 j = 1 4 k = 1 ( y .. k y ... ) 2 Geno 3 i = 1 4 j = 1 4 k = 1 ( y i .. y ... ) 2 Blocks Geno 3 i = 1 4 j = 1 4 k = 1 ( y i . k y i .. y .. k + y ... ) 2 Fert 3 i = 1 4 j = 1 4 k = 1 ( y . j . y ... ) 2 Geno Fert 3 i = 1 4 j = 1 4 k = 1 ( y ij . y i .. y . j . + y ... ) 2 error 3 i = 1 4 j = 1 4 k = 1 ( y ijk y i . k y ij . + y i .. ) 2 C . Total 3 i = 1 4 j = 1 4 k = 1 ( y ijk y ... ) 2 c 2011Dept.Statistics(IowaStateUniversity) Stat511section19 5/22 E ( MS GENO )= FB G 1 G i = 1 E ( y i .. y ... ) 2 = FB G 1 G i = 1 E ( i . .. + w i . w .. + e i . e ... ) 2 = FB G i = 1 ( i . .. ) 2 G 1 + FBE G i = 1 ( w i . w .. ) 2 G 1 + FBE G i = 1 ( e i ....
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This note was uploaded on 02/11/2012 for the course STAT 511 taught by Professor Staff during the Spring '08 term at Iowa State.

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19SplitLME(1) - ANOVAANALYSISOFABALANCEDSPLIT-PLOT...

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