Randomized Complete Block Design RCBD n Blocka nuisance
Randomized Complete Block Design (RCBD) n Block--a nuisance factor included in an experiment to account for variation among eu’s n Presumably, eu’s are homogenous within a block n Treatments are randomly assigned to eu’s within each block
RCBD n The model and hypotheses
Blocks in RCBDs n 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 Discussion n There is some controversy as to whether fixed block effects should be tested – F test is considered at best approximate n Additivity of the block and factor effects – Error includes lack-of-fit – Practical considerations n Both block and factor could have a factorial structure
Missing values in RCBD’s Missing values result in a loss of orthogonality (generally) n A single missing value can be imputed n – The missing cell (yi*j*=x) can be estimated by profile least squares
Imputation n The error df should be reduced by one, since x was estimated n SAS can compute the F statistic, but the pvalue will have to be computed separately n The method is efficient only when a couple cells are missing
Alternate Imputation approaches n The usual Type III analysis is available, but be careful of interpretation n Little and Rubin use MLE and simulationbased approaches n PROC MI in SAS v 9 implements Little and Rubin approaches
Power analysis n Power calculations change little – b replaces n in formulas – The error df is (a-1)(b-1)
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