Flipped Assignment 18

1.a Design of 2^3 Factorial

where factors= 3

levels = 2

Replicate run = 1

Effect ABC

1.b Corner Points


Block 1 ( Negative ABC) - [(1), ab, ac, bc ]
Block 2 (Positive ABC) - [a, b, c , abc ]

2.a

If the Design is to be run in 4 blocks then the confounded blocks will be

Effect AB , AC & BC.

2.b Design for 4 blocks

Block #1 [(1), abc]

Block#2 [(a), bc]

Block#3 [(b), ac]

Block#4 [(c), ac]

3.a Half Normal Plot

A<-c(-1,1,-1,1,-1,1,-1,1)
B<-c(-1,-1,1,1,-1,-1,1,1)
AB<-c(1,-1,-1,1,1,-1,-1,1)
C<-c(-1,-1,-1,-1,1,1,1,1)
AC<-c(1,-1,1,-1,-1,1,-1,1)
BC<-c(1,1,-1,-1,-1,-1,1,1)
ABC<-c(-1,1,1,-1,1,-1,-1,1)
tl<-c(22,32,35,55,44,40,60,39)
Data<-data.frame(A,B,AB,C,AC,BC,ABC)

#Half Normal Plot:

library(DoE.base)
## Warning: package 'DoE.base' was built under R version 4.5.2
## Loading required package: grid
## Loading required package: conf.design
## Warning: package 'conf.design' was built under R version 4.5.2
## Registered S3 method overwritten by 'DoE.base':
##   method           from       
##   factorize.factor conf.design
## 
## Attaching package: 'DoE.base'
## The following objects are masked from 'package:stats':
## 
##     aov, lm
## The following object is masked from 'package:graphics':
## 
##     plot.design
## The following object is masked from 'package:base':
## 
##     lengths
mod <- lm(tl~A*B*C,data = Data)
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)

## no significant effects

#As per the half normal plot none of the factors appears to be significant
at alpha = 0.05

3.b

# The cofficient interaction ABC is -3.375 and since abc is not significant the block is also not significant