Write up a statistics problem that describes a single-factor design, preferably involving unicorns, glitter, zombies, aliens, or some combination of these things. Design your scenario so that your theoretically-driven hypotheses take the form of three or more orthogonal single-df planned comparisons. You get 4 points for writing a scenario that meets these criteria. Please be sure to explain the motivation for your hypotheses.
a. Demonstrate that the contrasts are orthogonal.
b. Generate your data for this problem in SAS. Generate your data in a manner that is consistent with the assumptions and linear model associated with the one-way ANOVA.