Artificial heart valves were tested in a mechanical apparatus which measured and controlled the pulse rate and the blood pressure of the heart. The purpose of the experiment was to determine the best valve type of the four studied. The maximum flow gradient (in mm Hg) is the dependent variable for each trial.
The dependent variable is "Flow," the maximum flow gradient. The factors are "Type" (valve type), "Valve" (valve number of that "Type") and "Pulse".
In this design "Valve" is nested within "Type". The four valve types are treatments whose order of testing on the machine is randomized, with each valve type ("Type") occuring twice, each time with a different valve ("Valve") of that type. We anticipate interactions, so we should include two-way interactions among the variables. Note that "Type" and "Valve" cannot interact because Valve is nested in Type.
This model exhausts all the degrees of freedom leaving none for the error term, so the F-ratios for "Valve" and for the Valve*Pulse interaction cannot be estimated.