Why would we expect the log transformation to be the variance-stabilizing transformation for the data in Exercise 6.2?
Exercise 6.2
Bacteria in solution are often counted by a method known as serial dilution plating. Petri dishes with a nutrient agar are inoculated with a measured amount of solution. After 3 days of growth, an individual bacterium will have grown into a small colony that can be seen with the naked eye. Counting original bacteria in the inoculum is then done by counting the colonies on the plate. Trouble arises because we don't know how much solution to add. If we get too many bacteria in the inoculum, the petri dish will be covered with a lawn of bacterial growth and we won't be able to identify the colonies. If we get too few bacteria in the inoculum, there may be no colonies to count. The resolution is to make several dilutions of the original solution (1:1, 10:1, 100:1, and so on) and make a plate for each of these dilutions. One of the dilutions should produce a plate with 10 to 100 colonies on it, and that is the one we use. The count in the original sample is obtained by multiplying by the dilution factor. Suppose that we are trying to compare three different Pasteurization treatments for milk. Fifteen samples of milk are randomly assigned to the three treatments, and we determine the bacterial load in each sample after treatment via serial dilution plating. The following table gives the counts.
Test the null hypothesis that the three treatments have the same effect on bacterial concentration.
