Sleuth3 (version 0.1-6)

case1701: Magnetic Force on Printer Rods

Description

Engineers manipulated three factors (with 3, 2, and 4 levels each) in the construction and operation of printer rods, to see if they influenced the magnetic force around the rod.

Usage

case1701

source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

Examples

str(case1701)
attach(case1701)
   
## EXPLORATION
MagneticForces  <- cbind(L1,L2,L3,L4,L5,L6,L7,L8,L9,L10,L11)
mfCor <- cor(MagneticForces)
round(mfCor,2)  # Show correlations, rounded to two digits 

mfPca     <- prcomp(MagneticForces)  # principal components 
summary(mfPca) # Show the proportion of variance explained by each PC
plot(mfPca)  # Graph proportion of variances explained by each PC (Scree Plot)
mfCoefs   <- mfPca$rotation   # Extract the coefficients
dim(mfCoefs)  #   #11 rows and 11 columns
round(mfCoefs[,1:3],3)  # Show the first 3 columns of the score matrix, rounded 

# Explore a possible meaningful linear combination suggested by first PC  
round(mfCoefs[,1],1)  # Show coefficients of 1st pc, rounded to 1 digit  
# Coefficients are all very similar, suggesting a constant coefficient; use 1/11 
mfAve     <- (L1 + L2 + L3 + L4 + L5 + L6 + L7 + L8 + L9 + L10 + L11)/11
mfScores  <- mfPca$x
pc1       <- mfScores[,1] #Values for first principal component of MagneticForces
cor(mfAve,pc1) # correlation of the average and the first PC (=0.999567)
plot(pc1 ~ mfAve)

# Explore a possible meningful linear combination suggested by second PC 
round(mfCoefs[,2],1) # Show coefficients of 2nd pc, rounded to 1 digit 
# Second set of coefficients are negative on the left end of the rod and 
# positive on the right end. Try Ave(L9 + L10 + L11) - Ave(L1 + L2 + L3). 
mfEnds    <- (L9 + L10 + L11)/3 - (L1 + L2 + L3)/3    
pc2       <- mfScores[,2]
residualEnds  <- lm(mfEnds ~ mfAve)$residual # Ends with average effect removed
plot(pc2 ~ residualEnds)
cor(residualEnds, pc2)                 # 0.973
 
# Explore a possible meaningful linear combination suggested by third PC
round(mfCoefs[,3],1)  # Show doefficients of 3rd pc, rounded to 1 digit
# Try a contrast between the first 4 positions and the 6th position
mfPeak    <- (L1 + L2 + L3 + L4)/4 - L6
pc3       <- mfScores[,3]
residualPeak <- lm(mfPeak ~ mfAve + mfEnds)$residual
plot(pc3 ~ residualPeak)
cor(residualPeak,pc3)           # 0.971
# Note: the variation explained by the third PC seems to be due almost entirely 
# to one printer rod. (Keep this in mind.)


## INFERENCE:  ANALYSIS OF EXPERIMENTAL FACTORS ON 3-DIMENSIONAL RESPONSE
myResponse  <- cbind(mfAve, mfEnds, mfPeak)
cor(myResponse)
myLm1     <- lm(myResponse ~ Current + Config + Material)
anova(myLm1)  # Noticeable effect of Current but not Config or Material

plot(mfAve ~ Current)
myLm2   <- lm(mfAve ~ Current)
abline(myLm2)                         
summary(myLm2)  # No evidence of an effect of current on average magnetic force

plot(mfEnds ~ Current)
myLm3   <- lm(mfEnds ~ Current)
abline(myLm3)
summary(myLm3)  # Evidence that Current effects the difference in MF at the ends

plot(mfPeak ~ Current)
myLm4   <- lm(mfPeak ~ Current)
abline(myLm4)
summary(myLm4)  # No evidence of an effect of Current on peak MF in the center


## GRAPHICAL DISPLAY FOR PRESENTATION
plot(mfEnds ~ jitter(Current,.1),
  xlab="Electrical Current Used in Printer Rod Manufacture (milliamperes)" ,
  ylab="Magnetic Force at Positions 9-11 Minus Magnetic Force at Positions 1-3",
  main="Effect of Electrical Current on Magnetic Force Surrounding Printer Rod",
  col="black", pch=21, lwd=2,  bg="green", cex=2 )   
abline(myLm3,
  lwd=2)

detach(case1701)