Data set: Popcorn
a. Use the data structure of the three-way factorial design to write a statistical model for the micro-wave popcorn study. Since there are three factors of interest in the study, the model will need three terms, such as αi, βj, and γk, to represent each main effect and interaction effect. Use yijkl to represent an individual observation.
b. Table 4.9 gives a three-way ANOVA table. Fill in the formulas for SSC, SSBC, MSC, MSBC, and the F-statistic.
Table 4.9 Three-way ANOVA Table.

c. Calculate the effect sizes for Brand, Microwave, and Time. Create a main effects plot and explain how the graph helps us to visualize the effect size.
d. Calculate the effects for the Brand*Microwave interaction. Show your work in calculating only the Fastco*Room interaction effect by hand. Clearly interpret the meaning of these effects as it relates to this experiment.

MS F-Statistic MSA MSE SSA MSE SSAB df MSAB MSE AB 1) AC ( IK 1) BC (J (K 1) MSAB MSE df SSE Error subtraction subtraction MSE = df JK L Total cif