We made the point in Sect XXXXXXXXXXthat a log transformation would not alleviate nonnormality. Yet we model the log of the mean response. Let us consider the differences. (1) First consider the small...

We made the point in Sect. 8.1.1 that a log transformation would not alleviate nonnormality. Yet we model the log of the mean response. Let us consider the differences.

(1) First consider the small data set consisting of 0, 1, 0, 3, 1. What is the mean? What is the log of the mean? What is the mean of the logs of each data point?

(2) Even if there are no zeros, these two operations are quite different. Consider the small data set consisting of 2, 3, 32, 7, 11. What is the log of the mean? What is the mean of the logs of the data? Why are they different?

(3) Repeat the above calculation, but using medians.