12%20Competing%20Design%202_21_08

12%20Competing%20Design%202_21_08 - Two Designs for...

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1 1 Choosing between Competing Experimental Designs Peng Liu 2/21/2008 2 Two Designs for Comparing Two Treatments 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 Design 2 Design 1 3 Design 1: Mixed Linear Model for a Single Gene Y 1111 = μ + τ 1 + δ 1 +s 1 +b 11 +e 1111 Y 1221 = μ + τ 1 + δ 2 +s 2 +b 11 +e 1221 Y ijkl = μ + τ i + δ j +s k +b il +e ijkl Y 1132 = μ + τ 1 + δ 1 +s 3 +b 12 +e 1132 Y 1242 = μ + τ 1 + δ 2 +s 4 +b 12 +e 1242 Y 1153 = μ + τ 1 + δ 1 +s 5 +b 13 +e 1153 Y 1263 = μ + τ 1 + δ 2 +s 6 +b 13 +e 1263 Y 1174 = μ + τ 1 + δ 1 +s 7 +b 14 +e 1174 Y 1284 = μ + τ 1 + δ 2 +s 8 +b 14 +e 1284 Y 2211= μ + τ 2 + δ 2 +s 1 +b 21 +e 2211 Y 2121 = μ + τ 2 + δ 1 +s 2 +b 21 +e 2121 Y 2232 = μ + τ 2 + δ 2 +s 3 +b 22 +e 2232 Y 2142 = μ + τ 2 + δ 1 +s 4 +b 22 +e 2142 Y 2253 = μ + τ 2 + δ 2 +s 5 +b 23 +e 2253 Y 2163 = μ + τ 2 + δ 1 +s 6 +b 23 +e 2163 Y 2274 = μ + τ 2 + δ 2 +s 7 +b 24 +e 2274 Y 2184 = μ + τ 2 + δ 1 +s 8 +b 24 +e 2184 4 Design 2: Mixed Linear Model for a Single Gene Y 1111 = μ + τ 1 + δ 1 +s 1 +b 11 +e 1111 Y 1222 = μ + τ 1 + δ 2 +s 2 +b 12 +e 1222 Y ijkl = μ + τ i + δ j +s k +b il +e ijkl Y 1133 = μ + τ 1 + δ 1 +s 3 +b 13 +e 1133 Y 1244 = μ + τ 1 + δ 2 +s 4 +b 14 +e 1244 Y 1155 = μ + τ 1 + δ 1 +s 5 +b 15 +e 1155 Y 1266 = μ + τ 1 + δ 2 +s 6 +b 16 +e 1266 Y 1177 = μ + τ 1 + δ 1 +s 7 +b 17 +e 1177 Y 1288 = μ + τ 1 + δ 2 +s 8 +b 18 +e 1288 Y 2211= μ + τ 2 + δ 2 +s 1 +b 21 +e 2211 Y 2122 = μ + τ 2 + δ 1 +s 2 +b 22 +e 2122 Y 2233 = μ + τ 2 + δ 2 +s 3 +b 23 +e 2233 Y 2144 = μ + τ 2 + δ 1 +s 4 +b 24 +e 2144 Y 2255 = μ + τ 2 + δ 2 +s 5 +b 25 +e 2255 Y 2166 = μ + τ 2 + δ 1 +s 6 +b 26 +e 2166 Y 2277 = μ + τ 2 + δ 2 +s 7 +b 27 +e 2277 Y 2188 = μ + τ 2 + δ 1 +s 8 +b 28 +e 2188
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2 5 Design 2: Mixed Linear Model for a Single Gene Y 1111 = μ + τ 1 + δ 1 +s 1 +b 11 +e 1111 Y 1222 = μ + τ 1 + δ 2 +s 2 +b 12 +e 1222 Note that b and e are completely confounded in Design 2. Thus we would use only one random residual term for both factors, but we write the terms separately here for the sake of comparison with Design 1. Y 1133 = μ + τ 1 + δ 1 +s 3 +b 13 +e 1133 Y 1244 = μ + τ 1 + δ 2 +s 4 +b 14 +e 1244 Y 1155 = μ + τ 1 + δ 1 +s 5 +b 15 +e 1155 Y 1266 = μ + τ 1 + δ 2 +s 6 +b 16 +e 1266 Y 1177 = μ + τ 1 + δ 1 +s 7 +b 17 +e 1177 Y 1288 = μ + τ 1 + δ 2 +s 8 +b 18 +e 1288 Y 2211= μ + τ 2 + δ 2 +s 1 +b 21 +e 2211 Y 2122 = μ + τ 2 + δ 1 +s 2 +b 22 +e 2122 Y 2233 = μ + τ 2 + δ 2 +s 3 +b 23 +e 2233 Y 2144 = μ + τ 2 + δ 1 +s 4 +b 24 +e 2144 Y 2255 = μ + τ 2 + δ 2 +s 5 +b 25 +e 2255 Y 2166 = μ + τ 2 + δ 1 +s 6 +b 26 +e 2166 Y 2277 = μ + τ 2 + δ 2 +s 7 +b 27 +e 2277 Y 2188 = μ + τ 2 + δ 1 +s 8 +b 28 +e 2188 6 Test of Interest ± H 0 : τ 1 = τ 2 vs. H A : τ 1 = τ 2 ± Equivalent to H 0 : τ 1 - τ 2 = 0 vs. H A : τ 1 - τ 2 = 0 ± We estimate τ 1 - τ 2 by Y 1 ...-Y 2 ... ± Y 1 ...-Y 2 ...= τ 1 - τ 2 + b 1 .- b 2 . + e 1 ... - e 2 ... 7 Design 1 Estimate of τ 1 - τ 2 Y 1 ...= μ + τ 1 + δ .+s.+b 1 .+e 1 ... Y 2 ...= μ + τ 2 + δ .+s.+b 2 .+e 2 ... Y 1111 = μ + τ 1 + δ 1 +s 1 +b 11 +e 1111 Y 1221 = μ + τ 1 + δ 2 +s 2 +b 11 +e 1221 Y 1132 = μ + τ 1 + δ 1 +s 3 +b 12 +e 1132 Y 1242 = μ + τ 1 + δ 2 +s 4 +b 12 +e 1242 Y 1153 = μ + τ 1 + δ 1 +s 5 +b 13 +e 1153 Y 1263 = μ + τ 1 + δ 2 +s 6 +b 13 +e 1263 Y 1174 = μ + τ 1 + δ 1 +s 7 +b 14 +e 1174 Y 1284 = μ + τ 1 + δ 2 +s 8 +b 14 +e 1284 Y 2211= μ + τ 2 + δ 2 +s 1 +b 21 +e 2211 Y 2121 = μ + τ 2 + δ 1 +s 2 +b 21 +e 2121 Y 2232 = μ + τ 2 + δ 2 +s 3 +b 22 +e 2232 Y 2142 = μ + τ 2 + δ 1 +s 4 +b 22 +e 2142 Y 2253 = μ + τ 2 + δ 2 +s 5 +b 23 +e 2253 Y 2163 = μ + τ 2 + δ 1 +s 6 +b 23 +e 2163 Y 2274 = μ + τ 2 + δ 2 +s 7 +b 24 +e 2274 Y 2184 = μ + τ 2 + δ 1 +s 8 +b 24 +e 2184 Average over 4 effects Y 1 ... - Y 2 ... = τ 1 - τ 2 + b 1 .- b 2 . + e 1 ... - e 2 ...
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This note was uploaded on 08/26/2009 for the course STAT 416 taught by Professor Peng,l during the Spring '08 term at Iowa State.

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12%20Competing%20Design%202_21_08 - Two Designs for...

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