Multifactorial mixed (M)ANOVA
Alertness was measured on a scale of 0 to 50, an aggregate score on a battery of tests for reaction time, concentration, and wakefulness (a higher number means more alertness).
Inspecting the first MANOVA commands, (a) comment on what each of the commands does and (b) choose contrasts and justify your choice.
(a) Run the first MANOVA, but only inspect the means right now and draw a graph. You can do this either by hand or in a program such as EXCEL. An example of how to generate EXCEL cell means and (if you want them, pure interaction graphs) is provided here.(b) Looking at the means and graph, what patterns do you detect in the data? What main effects, interactions, or simple effects would you expect to be substantial? Given the nature of the TIME factor, pure interactions may be too difficult to interpret. (Please include the graph in your homework file.)
(a) Using the decision tree on within-subject ANOVA, describe which methods of analysis are available and why. (b) Argue for the most prudent method. (c) Briefly report the major omnibus results and comment on the limitations of interpreting these results. (d) Also briefly examine the other analysis methods (e.g., average-F or univariate F, if you chose multivariate); do the results differ by method?
Now focus on the particular contrasts you chose and interpret them (it's helpful to return to your graphs). Begin with the straightforward two contrasts for DOSE. Then note that the DOSE x TIME multivariate test (omnibus test) has two possible discriminant functions (because k -1 for the b/s factor DOSE is 2). This omnibus test is normally difficult to interpret, so focus instead on the two constituent multivariate contrasts (which come right after the omnibus test, thanks to the SINGLEDF subcommand). Make sure you interpret the interaction (or lack thereof) correctly. Then examine and interpret the TIME main effect (or lack thereof). This one has only one discriminant function with two contrasts. (That's because the main effect of a within-subject factor tests whether the whole set of contrasts is different from zero, so you need only one discriminant function to answer this question.)
(a) Now run the second analysis, a mouthful of 2 (INFORM) x 3 (DOSE) x 3 (TIME) between-within mixed multivariate design. Here we add a second between-subjects factor, called INFORM: Half of the people were informed about the dose of caffeine they received, the other half was uninformed. (b) As before, first inspect the means and draw graphs. Because we now have three factors, you will need several different tables, removed main effects, and graphs to correctly display the distinct 2-way interactions (and the one 3-way interaction). Note: Interactions involving the multivariate TIME factor should not be subjected to the main-effect removal procedure. Try to interpret the entire multivariate patterns (how TIME contrasts differentiate between groups), as indicated by the corresponding multivariate test and the graphed means. What effects would you expect to be substantial? [For parts (b) and (c) you may choose to go the simple-effects route, in which case you need to tell SPSS to give you simple-effects output. The appropriate commands are in the /DESIGN or /WSDESIGN lines, and you will have to look at next week's lecture and the SPSS handout from the readings to get more detail.]
(a) Choose the multivariate method of analysis and identify and describe all effects with p < .01 (to hold the analysis-wise alpha below .10). (b) Use discriminant functions for your various contrasts to interpret the exact nature of the effects. Things get complicated here, so keep careful track of which effects are worth interpreting, what contrasts constitute them, and how we can best understand them.
Write your one-page summary of analyses and results on the second (three-way) MANOVA only.