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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. $\endgroup$ Jan 2, 2022 at 13:54

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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         
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