1 1. RCBD Assignment

Linear effect equation:

\[ _{Yij=\mu +\tau _{i}+\beta _{j}+\epsilon _{ij}} \]

Null hypotheses = \(H_{0}:\mu_{ 1}=\mu_{ 2}=\mu_{ 3}=\mu_{ 4}\)

Alternative Hypotheses = Atleast one mu differs

Question 1:

Chemical <- c(rep(1,5),rep(2,5),rep(3,5),rep(4,5))
Bolt <- rep(seq(1,5),4)
Obs <- c(73,68,74,71,67,73,67,75,72,70,75,68,78,73,68,73,71,75,75,69)
dat <- data.frame(Chemical,Bolt,Obs)
library(GAD)
Chemical <- as.fixed(Chemical)
Bolt <- as.fixed(Bolt)
model <- lm(Obs~Chemical+Bolt)
gad(model)
## Analysis of Variance Table
## 
## Response: Obs
##          Df Sum Sq Mean Sq F value    Pr(>F)    
## Chemical  3  12.95   4.317  2.3761    0.1211    
## Bolt      4 157.00  39.250 21.6055 2.059e-05 ***
## Residual 12  21.80   1.817                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

P-value is less than alpha 0.15, reject Ho.

Quest tion 2:

Conduct the analysis without blocking

model1 <- lm(Obs~Chemical)
gad(model1)
## Analysis of Variance Table
## 
## Response: Obs
##          Df Sum Sq Mean Sq F value Pr(>F)
## Chemical  3  12.95  4.3167  0.3863 0.7644
## Residual 16 178.80 11.1750

P-value is greater than alpha, we don’t have evidence to reject the Ho hypothesis

Question 3:

In question 1, we have more power to reject the Ho by adding block in our experiment design. In question 2 doesn’t have blocking so the sum of square of blocking is added into the sum of square error making it less power.

2 Complete R Code

It is a good idea to include this at the end of every RMarkdown document

#Model with Block
Chemical <- c(rep(1,5),rep(2,5),rep(3,5),rep(4,5))
Bolt <- rep(seq(1,5),4)
Obs <- c(73,68,74,71,67,73,67,75,72,70,75,68,78,73,68,73,71,75,75,69)
dat <- data.frame(Chemical,Bolt,Obs)
library(GAD)
Chemical <- as.fixed(Chemical)
Bolt <- as.fixed(Bolt)
model <- lm(Obs~Chemical+Bolt)
gad(model)

#Model without the block

model1 <- lm(Obs~Chemical)
gad(model1)