14.3.

A manufacturing engineer is studying the dimensional variability of a particular component that is produced on three machines. Each machine has two spindles, and four components are randomly selected from each spindle. The results follow. Analyze the data, assuming that machines and spindles are fixed factors.

According to Dr.Matis’s video(7:19;Nested Factors in R), it is not possible to perform the question the way the book asks us to in this problem, as we cannot have our nested factor as fixed and must set it to random instead

library(GAD)
Machine <- as.fixed(c(rep(1,8),rep(2,8),rep(3,8)))
Spindle <- as.random(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)
model <- aov(obs~Machine+Spindle%in%Machine)
gad(model)
## 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

We can see using the GAD package that the spindle types within the machines are significant, though which machine it is isn’t significant.

par(mfcol=c(2,2))
plot(model)

Our plots look normal and no assumptions have been violated that I can tell. This model seems adequate.

All Code Used

library(GAD)
Machine <- as.fixed(c(rep(1,8),rep(2,8),rep(3,8)))
Spindle <- as.random(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)
model <- aov(obs~Machine+Spindle%in%Machine)
gad(model)

par(mfcol=c(2,2))
plot(model)