Learn about Randomized Complete Block Design (RCBD), a statistical design used in experiments to reduce variation among experimental units. Discover how blocks, fixed and random effects, missing value imputation, and power analysis play crucial roles in RCBD experiments.
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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 , 0 ( = + + + N + , Y ij i j ij ij + 2 ) iid ij ij : 0 H o i
Blocks in RCBDs 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 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 RCBDs 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 ' . * a + ' b ' ay by y . * .. i j = x ( )( ) 1 1
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
Alternate Imputation approaches 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 2 bL = = For H : , 0 use L o 2 2 ic 2 i b , 0 = = For H : use o 2 The error df is (a-1)(b-1)
