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Randomized Complete Block Design (RCBD). Block--a nuisance factor included in an experiment to account for variation among eu’s Presumably, eu’s are homogenous within a block Treatments are randomly assigned to eu’s within each block. RCBD. The model and hypotheses. RCBD.

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randomized complete block design rcbd
Randomized Complete Block Design (RCBD)
  • Block--a nuisance factor included in an experiment to account for variation among eu’s
  • Presumably, eu’s are homogenous within a block
  • Treatments are randomly assigned to eu’s within each block
slide2
RCBD
  • The model and hypotheses
slide3
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
slide4
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
missing values in rcbd s
Missing values in RCBD’s
  • Missing values result in a loss of orthogonality (generally)
  • A single missing value can be imputed
    • The missing cell (yi*j*=x) can be estimated by profile least squares
imputation
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
imputation1
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
power analysis
Power analysis
  • Power calculations change little
    • b replaces n in formulas
    • The error df is (a-1)(b-1)
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