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19.5EMS(1) - Two approaches for E MS RCBD with random...

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Two approaches for E MS RCBD with random blocks and multiple obs. per block Y ijk = μ + β i + τ j + βτ ij + ijk where i ∈ { 1 , . . . , B } , j ∈ { 1 , . . . , T } , k ∈ { 1 , . . . , N } . with ANOVA table: Source df R Blocks B-1 Treatments T-1 R Block × Trt (B-1)(T-1) R Error BT(N-1) C. total BTN - 1 c 2011 Dept. Statistics (Iowa State University) Stat 511 section 19.5 1 / 7 Expected Mean Squares from two different sources Source 1: Searle (1971) 2: Graybill (1976) Blocks σ 2 e + N σ 2 p + NT σ 2 B η 2 e + NT η 2 B Treatments σ 2 e + N σ 2 p + Q ( τ ) η 2 e + N η 2 p + Q ( τ ) Block × Trt σ 2 e + N σ 2 p η 2 e + N η 2 p Error σ 2 e η 2 e 1: Searle, S (1971) Linear Models 2: Graybill, F (1976) Theory and Application of the Linear Model . Same except for Blocks Different F tests for Blocks EMS 1: MS Blocks / MS Block*Trt EMS 2: MS Blocks / MS Error c 2011 Dept. Statistics (Iowa State University) Stat 511 section 19.5 2 / 7 Can find “rules” for computing coefficients in EMS Rules generally give EMS 2, e.g. Schulz (1954, Biometrics), Cornfield-Tukey (1956, Ann. Math. Stat.) Long-standing controversy / disagreement
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