1. (DVD #12.6) Video game experiment

Professor Robert Wardrop, of the University of Wisconsin, conducted an experiment in 1991 to evaluate in which of five sound modes he best played a certain video game. The first three sound modes corresponded to three different types of background music, as well as game sounds expected to enhance play. The fourth mode had game sounds but no background music. The fifth mode had no music or game sounds. Denote these sound modes by the treatment factor levels 1–5, respectively. 

The experimenter observed that the game required no warm-up, that boredom and fatigue would be a factor after 4–6 games, and that his performance varied considerably on a day-to-day basis. Hence, he used a Latin square design, with the two blocking factors being “day” and “time order of the game.” The response measured was the game score, with higher scores being better. The design and resulting data are given in Table 12.16. 

A. Write down a possible model for these data. If the assumptions appear to be approximately satisfied, then answer parts (b)–(f). 

B. Plot the data and discuss the plot. 

C. Complete an analysis of variance table and check the model assumptions. 

D. Evaluate whether blocking was effective. 

E. Construct simultaneous 95% confidence intervals for all pairwise comparisons, as well as the “music versus no music” contrast 

1/3(τ1 +τ2 +τ3) − 1/2(τ4 +τ5) 

and the “game sound versus no game sound” contrast 

1/4( τ 1 + τ 2 + τ 3 + τ 4 ) − τ 5 . 

F. What are your conclusions from this experiment? Which sound mode(s) should Professor Wardrop use?