1 Blocking in a 2^k Factorial Design

Question 3:

  1. Which effects appear to be significant?

Input data:

library(DoE.base)
A<-c(-1,1,-1,1,-1,1,-1,1)
B<-c(-1,-1,1,1,-1,-1,1,1)
C<-c(-1,-1,-1,-1,1,1,1,1)

obs<-c(22,32,35,55,44,40,60,39)
dat<-data.frame(A,B,C,obs)
mod<-lm(obs~A*B*C,data=dat)

Display the coeficient and the halfnormal plot:

coef(mod)
## (Intercept)           A           B           C         A:B         A:C 
##      40.875       0.625       6.375       4.875      -0.875      -6.875 
##         B:C       A:B:C 
##      -2.625      -3.375
halfnormal(mod)

As shown in the halfnormal plot, none of the effect are significant.

  1. Does it appear that the block was significant?

The blocks are confounded with effect of AB, AC, BC and these effect are not significant as shown in the halfnormal plot => the block was not significant.

2 Complete R Code

#Input data
library(DoE.base)
A<-c(-1,1,-1,1,-1,1,-1,1)
B<-c(-1,-1,1,1,-1,-1,1,1)
C<-c(-1,-1,-1,-1,1,1,1,1)

obs<-c(22,32,35,55,44,40,60,39)
dat<-data.frame(A,B,C,obs)
mod<-lm(obs~A*B*C,data=dat)
#Display coeficient and halfnormal plot
coef(mod)

halfnormal(mod)