I have learned about repeated measures ANOVA but is it possible to have a repeated measures factorial design? So if you have factor A with 2 levels and factor B with 2 levels where each combination has 2 units and each unit is measured three times. Is there another name for this design? Would there be a total of 23 degrees of freedom?
Yes, it's possible, but it's hard to get a time trend factor, it might be easier as a multilevel model. You can do this with SAS proc mixed:
proc mixed data = mydata; class unit A B; model outcome = A B time ; repeated /subject = unit type = cs rcorr; run;
The data should be in long format, so outcome is your outcome variable, and unit identifies the unit - each unit will have three rows in the dataset.
You might want to add A*B to the model line (but you're going to be close to running out of degrees of freedom).
You could also treat time as categorical by adding it to the class line.
Sometimes I like to play with a simpler model, to test that they really are equivalent:
proc mixed data = mydata; class unit time; model outcome = time ; repeated /subject = unit type = cs rcorr; run;
This model is just a repeated measures anova, with time as the only factor. You should get the same (or very nearly the same) answer doing it both ways.