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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


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 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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