Set Up

Here the experiment is set up

A <- c(1,2)
B <- c(1,1,2,2,3,3)

Spindle <- c(rep(A,12))
Machine <- c(rep(B,4))
obs <- c(12, 8 ,14, 12, 14, 16,
         9, 9, 15, 10, 10, 15,
         11, 10, 13, 11, 12, 15,
         12, 8, 14, 13, 11, 14)
Machine <- as.fixed(Machine)
Spindle <- as.random(Spindle)

As a nested effect spindle is set to random. Machine is a fixed effect.

Running the Experiment & Analysis

model <- lm(obs ~ Machine + Spindle %in% Machine)
summary(model)
## 
## Call:
## lm(formula = obs ~ Machine + Spindle %in% Machine)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
##  -2.00  -0.75   0.00   1.00   2.25 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        11.0000     0.6067  18.132  5.2e-13 ***
## Machine2            3.0000     0.8580   3.497  0.00258 ** 
## Machine3            0.7500     0.8580   0.874  0.39355    
## Machine1:Spindle2  -2.2500     0.8580  -2.622  0.01726 *  
## Machine2:Spindle2  -2.5000     0.8580  -2.914  0.00926 ** 
## Machine3:Spindle2   3.2500     0.8580   3.788  0.00135 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.213 on 18 degrees of freedom
## Multiple R-squared:  0.7897, Adjusted R-squared:  0.7313 
## F-statistic: 13.52 on 5 and 18 DF,  p-value: 1.45e-05

From the data analysis spindle 1 on machine 1, has the highest deviation, followed by machine 3 spindle 2.