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?


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)
mydata <- tibble(Blocks=as.factor(Blocks), T=as.factor(T), Y=rnorm(24, 10, 3))

mod0 <- lm(Y  ~ Blocks+T, data=mydata)
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               

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