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?
$\begingroup$ 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 ♦Jan 2, 2022 at 13:54
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