1. (Pizza study part 1) You see in the paper that a new pizza shop has opened, and the owners want to have a taste experiment to help them pick their signature pizzas. The owners are using Anchovies, Pineapple, and Sausage in different combinations, and they know that taste testers cannot eat 8 pizza samples. Therefore they have advertised that the first person to present them with a reasonable confounded block design where two blocks each get four combinations will get a free pizza.
a) You immediately decide to present them with a confounded block design in which the effect APS is confounded with blocks. Show which combinations go in each of the two blocks with this design.
b) Demonstrate that APS is confounded with blocks by writing the contrast for that effect and showing that each block has combinations that all have the same sign for this effect.
2. (Pizza study part 2) You arrive at the pizza shop only to find that one of your classmates has already presented them with a design confounding the AP effect. In an attempt to still get some free food, you offer to analyze the results from their taste test experiment. The data are in this file. Present the analysis of variance for the study, write a few sentences summarizing the results, and use plots to test model assumptions and display results. A higher score means better taste.
3. A researcher is studying five factors that are used in steel production in their factory, to see which are most important. Each factor will be measured at two levels in an experiment. Rather than collect data on all 32 combinations, the researcher wants to use a quarter fraction of the design, and she wants to use the defining relation I = BCDE = - ABDE. Show which eight combinations are to be included in the experiment, and show the aliases of every main effect and two-way interaction.