It is desired to use a randomized block design with $4$ blocks of size $6$ each for testing the effects of $5$ treatments A,B,C,D and E. In each block, treatments B,C,D and E are replicated once each, while treatment A replicated twice to ensure more precise estimation and testing for A. What will be the degree of freedom of treatments, blocks and error in this RBD model?
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$\begingroup$ Please add the self-study tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$– kjetil b halvorsen ♦Commented Jan 2, 2022 at 13:54
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1 Answer
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This looks like a self-study question, so I will limit myself to show how you can investigate yourself by simulating some data in R:
set.seed(7*11*13)# My public seed
Blocks <- rep(1:4, each=6)
T <- rep(rep(LETTERS[1:5], c(2, rep(1, 4))), 4)
library(tidyverse)
mydata <- tibble(Blocks=as.factor(Blocks), T=as.factor(T),
Y=rnorm(24, 10, 3))
mod0 <- lm(Y ~ Blocks + T, data=mydata)
anova(mod0)
Analysis of Variance Table
Response: Y
Df Sum Sq Mean Sq F value Pr(>F)
Blocks 3 12.142 4.0472 0.3098 0.8180
T 4 61.268 15.3171 1.1726 0.3598
Residuals 16 208.993 13.0621
answered Mar 20, 2020 at 23:50