The design in Exercise 11 is sometimes called a split-plot / repeated measures (SP/ RM) [1,2], where the 1 represents the number of whole-plot factors and the 2 represents the number of split-plot factors. In fact, the previous exercise provides only half of the data. In addition to the 16 females discussed in Exercise 11, 16 males were also tested. The complete design is a split-plot/ repeated measures (SP/ RM) [2, 2], with both gender and division as whole-plot factors.
a. Draw a Hasse diagram corresponding to this study, assuming that we are interested in all possible two-way interactions (do not include three-way interactions).
b. Calculate an appropriate ANOVA for this study, assuming that we are interested in testing all two-way interactions. Check the model assumptions and use an appropriate transformation if needed. Some software packages such as Minitab, do not easily analyze a split-plot design with two whole-plot factors. Instead create one new factor (Gender and Division) with 4 levels and use this as the one whole-plot factor in your ANOVA.
c. State your conclusions for this study. Provide appropriate plots and take into account random sampling and random allocation when stating your conclusions.