Data Preperation

yield <- c(12,18,13,16,17,15,20,15,10,25,13,24,19,21,17,23)
A <- c(-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1)
B <- c(-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1)
C <- c(-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1)  
D <- c(-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1)

Halfnormal Plot

dat <- data.frame(yield,A,B,C,D)

#install.packages("DoE.base")

library(DoE.base)
## Warning: package 'DoE.base' was built under R version 4.1.3
## Loading required package: grid
## Loading required package: conf.design
## 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
model1<- lm(yield ~ A*B*C*D,data = dat)
halfnormal(model1)
## 
## Significant effects (alpha=0.05, Lenth method):
## [1] A   A:C A:D D
abline(a= 0, b=1)

From the halfnormal plot it appears that factors A&D are significant along with interactions AC and AD

Factorial Analysis

The multifactor ANOVA is compiled below

model2 <- aov(yield~ A+C+D+A*C+A*D, data= dat) 
summary(model2)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## A            1  81.00   81.00  49.846 3.46e-05 ***
## C            1  16.00   16.00   9.846 0.010549 *  
## D            1  42.25   42.25  26.000 0.000465 ***
## A:C          1  72.25   72.25  44.462 5.58e-05 ***
## A:D          1  64.00   64.00  39.385 9.19e-05 ***
## Residuals   10  16.25    1.62                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

From the results of the multifactor anova all the tested effects (A,D,AC,AD) are significant at \(\alpha =.05\)