Video: Half-Normal Plots in R Example

Unreplicated 2^k Factorial Designs

In a process development study on yield, four factors were studied, each at two levels: time (A), concentration (B), pressure (C), and temperature (D).

a. Half-Normal Plot and Significance

The significant effects seem to be A, AC, AD, and D as shown in the half normal plot.

library(DoE.base) 
## 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
dat <- data.frame(  
  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),   
  Yield = c(12, 18, 13, 16, 17, 15, 20, 15, 10, 25, 13, 24, 19, 21, 17, 23) )  
mod <- lm(Yield ~ A * B * C * D, data = dat) 
coef(mod) 
##   (Intercept)             A             B             C             D 
##  1.737500e+01  2.250000e+00  2.500000e-01  1.000000e+00  1.625000e+00 
##           A:B           A:C           B:C           A:D           B:D 
## -3.750000e-01 -2.125000e+00  1.250000e-01  2.000000e+00 -1.027824e-16 
##           C:D         A:B:C         A:B:D         A:C:D         B:C:D 
## -1.595946e-16  5.000000e-01  3.750000e-01 -1.250000e-01 -3.750000e-01 
##       A:B:C:D 
##  5.000000e-01
halfnormal(mod)    
## 
## Significant effects (alpha=0.05, Lenth method):
## [1] A   A:C A:D D