TABLE OF CONTENTS Consider the problem of determining whether different brands of tires exhibit different amounts of tread loss after 20,000 miles of driving. A fleet manager wishes to consider four brands that are available and decide which brand is likely to show the least amount of tread wear after 20,000 miles. The brands to be considered are A, B, C, and D, and although driving conditions might be simulated in the laboratory, the manager wants to try these four brands under actual driving conditions. The variable to be measured is the difference in maximum tread thickness on a tire between the time it is mounted on the wheel of a car and after it has completed 20,000 miles on that car. The measured variable Y ij is this difference in thickness in mils (1 mil = 0.001 in.), and the only factor of interest is brands, say ? j, where j = 1,2,3, and 4.
Since the tires must be tried on cars, and since some measure of error is necessary, more than one tire of each brand must be used and a set of four of each brand would seem quite practical. This means 16 tires, four each of four different brands, and a reasonable experiment would involve at least four cars. Designating the cars as I, II, III, and IV, one might put brand A's four tires on car I, brand B's on car II, and so on, with a design as shown...
