# IOE366-Ch11-Addendum - Incomplete Blocking...

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Incomplete Blocking Experiment ignal) Design oise) (Signal) (Noise) actorial andomization Factorial Randomization ull ractional ested omplete Blocking Full Fractional Nested Complete 1 Complete Incomplete LATIN SQUARE DESIGNS • Blocking in Two Directions (Incomplete) B1 B2 B3 B4 A1 T1 T2 T3 T4 (p ) A2 A3 T4 T1 T2 T3 T3 T4 T1 T2 A4 T2 T3 T4 T1 Model: X ijk = μ + α i + β j + δ k + ε ijk where ε ijk ~ N(0, σ 2 ) df = (1) (I-1) (I–1) (I-1) (I–1)(I–2) 2 () ( ) ( ) ( ) ( )( ) i = 1,. ..,I j = 1,. ..,I k = 1,. ..,I LSD Example: Efficiency of Different Assembly Methods Order Operator Method Time Req'd 11C 1 0 4 1 2 D 14 13A7 14B8 21B7 8 2 2 C 18 23D 1 1 24A8 31A5 0 3 2 B 10 33C 1 1 34D9 41D 1 0 0 3 4 2 A 10 43B 1 2 44C 1 4 Results for Efficiency.MTW General Linear Model: Time versus Order, Operator, Method Factor Type Levels Values Order random 4 1 2 3 4 perator random 4 1 2 3 4 Operator random Method random 4 A B C D Analysis of Variance for Time, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Order 3 18.500 18.500 6.167 3.52 0.089 Operator 3 51.500 51.500 17.167 9.81 0.010 Method 3 72.500 72.500 24.167 13.81 0.004 Error 6 10.500 10.500 1.750 Total

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## This note was uploaded on 03/17/2010 for the course IOE 366 taught by Professor Garyherrin during the Winter '10 term at University of Michigan-Dearborn.

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IOE366-Ch11-Addendum - Incomplete Blocking...

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