The USGA is interested in knowing whether the difference in distance traveled by any two golf ball brands depends on the club used. Consequently, the USGA tests four different brands (A, B, C, D) of golf balls and two different clubs (driver, fiveiron) in a completely randomized design. Each of the eight Brand-Club combinations (treatments) is randomly and independently assigned to four experimental units, each experimental unit consisting of a specific position in the sequence of hits by Iron Byron.

The distance response is recorded for each of the 32 hits, and the results are shown in Table 9.13.

a. Use a statistical software package to partition the Total Sum of Squares into the components necessary to analyze this 4 * 2 factorial experiment.

b. Conduct the appropriate ANOVA tests and interpret the results of your analysis. Use α = .10 for each test you conduct.

c. If appropriate, conduct multiple comparisons of the treatment means. Use an experimentwise error rate of .10. Illustrate the comparisons with a graph.

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Table 9.13 Distance Data for 4 x 2 Factorial Golf Experiment Brand Club Driver Five-Iron A 226.4 232.6 234.0 220.7 163.8 179.4 168.6 173.4 B 238.3 231.7 227.7 237.2 184.4 180.6 179.5 186.2 C 240.5 246.9 240.3 244.7 179.0 168.0 165.2 156.5 D 219.8 228.7 232.9 237.6 157.8 161.8 162.1 160.3