Randomized Complete Block Design (RCBD)

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# Randomized Complete Block Design RCBD - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Randomized Complete Block Design RCBD' - hyman

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