a <- c(-1,1)
b <- c(-1,-1,1,1)
c <- c(-1,-1,-1,-1,1,1,1,1)
A <- c(rep(a,8))
B <- c(rep(b,4))
C <- c(rep(c,2))
D <- c(rep(-1,8),rep(1,8))
obs<- c(12,18,13,20,17,25,15,25,10,24,13,24,19,21,17,23)
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
mod <- lm(obs ~A*B*C*D)
halfnormal(mod)
##
## Significant effects (alpha=0.05, Lenth method):
## [1] A C A:C:D
From the half normal plot it appears that the Main effects of A and C are significant. While the ACD interaction is also significant.