Setup

Load Libraries Into Session

library(dplyr)
library(tidyr)
library(GAD)

Problem 14.3

Machine <- c(rep(1,8),rep(2,8),rep(3,8))
Spindle <- rep(c(rep(1,4),rep(2,4)),3)
Obs <- c(12,9,11,12,8,9,10,8,
         14,15,13,14,12,10,11,13,
         14,10,12,11,16,15,15,14)
dat14.3 <- data.frame(Machine,Spindle,Obs)
Machine <- as.fixed(Machine)
Spindle <- as.random(Spindle)
model14.3 <- lm(Obs~Machine+Spindle%in%Machine)
gad(model14.3)
## Analysis of Variance Table
## 
## Response: Obs
##                 Df Sum Sq Mean Sq F value    Pr(>F)    
## Machine          2  55.75 27.8750  1.9114 0.2915630    
## Machine:Spindle  3  43.75 14.5833  9.9057 0.0004428 ***
## Residual        18  26.50  1.4722                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

GAD results with the nested Spindle factor having a p-value of 0.0004 and the Machine factor having a p-value of 0.2916. Assuming \(\alpha=0.05\), the Spindle has a significant effect on dimensional variability and the Machine does not.