Randomized Complete Block Design (RCBD)

1
Randomized Complete Block Design (RCBD)

• Block--a nuisance factor included in an
  experiment to account for variation among eus
• Presumably, eus are homogenous within a block
• Treatments are randomly assigned to eus within
  each block

2
RCBD

• The model and hypotheses

3
RCBD

• Blocks can be modeled as both fixed and random
  effects (Soil example)
• Block Soil type (fixed or random?)
• Treatment Nitrogen x Watering Regimen
• Response IR/R reflection

4
RCBD

• There is some controversy as to whether fixed
  block effects should be tested
• F test is considered at best approximate
• Additivity of the block and factor effects
• Error includes lack-of-fit
• Practical considerations
• Both block and factor could have a factorial
  structure

5
Missing values in RCBDs

• Missing values result in a loss of orthogonality
  (generally)
• A single missing value can be imputed
• The missing cell (yijx) can be estimated by
  profile least squares

6
Imputation

• The error df should be reduced by one, since x
  was estimated
• SAS can compute the F statistic, but the p-value
  will have to be computed separately
• The method is efficient only when a couple cells
  are missing

7
Imputation

• The usual Type III analysis is available, but be
  careful of interpretation
• Little and Rubin use MLE and simulation-based
  approaches
• PROC MI in SAS v9 implements Little and Rubin
  approaches

8
Power analysis

• Power calculations change little
• b replaces n in formulas
• The error df is (a-1)(b-1)