Assignment 18

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

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

##    A  B AB  C AC BC ABC hrs
## 1 -1 -1  1 -1  1  1  -1  22
## 2  1 -1 -1 -1 -1  1   1  32
## 3 -1  1 -1 -1  1 -1   1  35
## 4  1  1  1 -1 -1 -1  -1  55
## 5 -1 -1  1  1 -1 -1   1  44
## 6  1 -1 -1  1  1 -1  -1  40
## 7 -1  1 -1  1 -1  1  -1  60
## 8  1  1  1  1  1  1   1  39

1.

1. Running this data in a 2-block design, we determined to confound interaction ABC, because it has the highest order interaction.

2. We would assign positive corner points to A,B,C, ABC, and negative corner points to interactions AB,AC,BC.

2.

1. For a 4-block design, we determine that AB,AC,BC interactions are confounded

2. Group by AB, AC pairs; each distinct pair defines a block:

• Block 1: AB=-1,AC=-1 -> A,BC

• Block 2: AB=-1,AC=1 -> B,AC

• Block 3: AB=1,AC=-1 -> C,AB

• Block 4: AB=1,AC=1 -> ABC

3.

model = lm(hrs~A*B*C, data=dat)
coef(model)

## (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(model)

## no significant effects

From the plots shown above, we determined that there are no significant effects or blocks.

Code Summary

library(DoE.base)
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)
hrs<-c(22,32,35,55,44,40,60,39)
dat<-data.frame(A,B,AB,C,AC,BC,ABC,hrs)
dat
model = lm(hrs~A*B*C, data=dat)
coef(model)
halfnormal(model)