# Kuehl+-+Chapter+8+Notes+-+Overheads+(06) - RCBD Using One...

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Chapter 8 Complete Block Designs 1 RCBD Using One Blocking Criterion Section 8.1 pp 263-264 In the designs we have looked at so far we have assumed that we have enough homogeneous experimental units to complete an experiment. What if we don’t have that many? One approach is to use some type of blocking. Note there are many blocking methods. We will look at complete blocks first. Any factor that affects the response variable in a non-homogeneous manner will increase the experimental error and decrease the precision of the experimental results. The point here is that the blocking increases the precision because it reduces and controls the experimental error variance. Successful blocking results in less variation among the units within the blocks than that among units from different blocks.

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Chapter 8 Complete Block Designs 2 Section 8.2 pp 264-275 We will start this with fixed blocks. Random blocks will discussed in turn. Plot design for an RCBD with six N rates (1-6) across a fixed irrigation gradient. Block 1 2 5 4 1 6 3 Irrigation Gradient Block 2 1 3 4 6 5 2 Block 3 6 3 5 1 2 4 Block 4 2 4 6 5 3 1 data a; input Block Nitrogen \$ NO3Content @@; cards; 1 2 40.89 1 5 37.99 1 4 37.18 1 1 34.98 1 6 34.89 1 3 42.07 2 1 41.22 2 3 49.42 2 4 45.85 2 6 50.15 2 5 41.99 2 2 46.69 3 6 44.57 3 3 52.68 3 5 37.61 3 1 36.94 3 2 46.65 3 4 40.23 4 2 41.90 4 4 39.20 4 6 43.29 4 5 40.45 4 3 42.91 4 1 39.97 ;;;; run;
Chapter 8 Complete Block Designs 3 The treatment and block effects are assumed to be additive which means they don’t interact. Source df FFR EMS 46 1 i j k Comp i B r-1 j N t-1 ij BN (r-1)*(t-1)? (ij)k e (r-1)*(t-1) Source df EMS 461 i j k Comp i B j N (ij)k e

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Chapter 8 Complete Block Designs 4 The Partition for (using the same notation as book) and the Sums of Square are: SS Total SS Trt SS Block SS Error or Residual
Chapter 8 Complete Block Designs 5 Proc Mixed data=A Method=type3; Class Block Nitrogen; Model NO3Content = Nitrogen Block; lsmeans Nitrogen / pdiff=control('4') cl adjust=dunnett; run; The Mixed Procedure Model Information Data Set WORK.A Dependent Variable NO3Content Covariance Structure Diagonal Estimation Method Type 3 Residual Variance Method Factor Fixed Effects SE Method Model-Based Degrees of Freedom Method Residual Class Level Information Class Levels Values Block 4 1 2 3 4 Nitrogen 6 1 2 3 4 5 6

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Chapter 8 Complete Block Designs 6 Dimensions Covariance Parameters 1 Columns in X 11 Columns in Z 0 Subjects 1 Max Obs Per Subject 24 Number of Observations Number of Observations Read Number of Observations Used Number of Observations Not Used 0 Type 3 Analysis of Variance Sum of Error Source DF Squares Mean Square Expected Mean Square Error Term DF F Pr > F Nitrogen 5 201.316383 40.263277 Var(Residual) + Q(Nitrogen) MS(Residual) 15 5.59 0.0042 Block 3 197.003933 65.667978 Var(Residual) + Q(Block) MS(Residual) 15 9.12 0.0011 Residual 15 108.008417 7.200561 Var(Residual) . . . .
Chapter 8 Complete Block Designs 7 Covariance Parameter Estimates Cov Parm Estimate Residual 7.2006 Fit Statistics -2 Res Log Likelihood 84.5 AIC (smaller is better) 86.5 AICC (smaller is better) 86.8 BIC (smaller is better) 87.2 Type 3 Tests of Fixed Effects Num Den Effect DF F Value Pr > F Nitrogen 5 15 5.59 0.0042 Block 3 9.12 0.0011

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