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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. RCBD. The model and hypotheses. RCBD.

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Randomized Complete Block Design (RCBD)

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  1. 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

  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 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

  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)

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