case0401 {Sleuth3}

Space Shuttle

Description

The number of space shuttle O-ring incidents for 4 space shuttle launches when the air temperatures was below 65 degrees F and for 20 space shuttle launches when the air temperature was above 65 degrees F.

Usage

case0401

Format

A data frame with 24 observations on the following 2 variables.

Incidents

the number of O-ring incidents

Launch

factor variable with two levels—"Cool" and "Warm"

Source

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

References

Feynman, R.P. (1988). What do You Care What Other People Think? W. W. Norton.

See Also

ex2011, ex2223

Examples

str(case0401)
attach(case0401)

mCool <- mean(Incidents[Launch=="Cool"]) 
mWarm <- mean(Incidents[Launch=="Warm"])
mDiff <- mCool - mWarm
c(mCool,mWarm,mDiff)  # Show the values of these variables

## PERMUTATION TEST , VIA REPEATED RANDOM RE-GROUPING (ADVANCED)
numRep  <- 50 # Number of random  groupings. CHANGE TO LARGER NUMBER; eg 50,000.   
rDiff   <- rep(0,numRep) # Initialize this variable to contain numRep 0s.
for (rep in 1:numRep) {  # Repeat the following commands numRep times:
  randomGroup <- rep("rWarm",24)  # Set randomGroup to have 24 values "rWarm"
  randomGroup[sample(1:24,4)]  <- "rCool"  # Replace 4 at random with "rCool"
  mW  <- mean(Incidents[randomGroup=="rWarm"]) # average of random "rWarm" group
  mC  <- mean(Incidents[randomGroup=="rCool"]) # average of random "rCool" group
  rDiff[rep] <- mC-mW  # Store difference in averages in 'rep' cell of rDiff
           }  # End of loop
hist(rDiff,  # Histogram of difference in averages from numRep random groupings
  main="Approximate Permutation Distribution",
  xlab="Possible Values of Difference in Averages",
  ylab="Frequency of Occurrence")
abline(v=mDiff)  # Draw a vertical line at the actually observed difference
pValue <- sum(rDiff >= 1.3)/numRep  # 1-sided p-value
pValue  
text(mDiff,75000, paste(" -->",round(pValue,4)), adj=-0.1) 

detach(case0401)