Functional Data Analysis in Designed Experiments

F-type tests for functional ANOVA models implicitly assume that the response curves are generated by a completely randomized design. By using the split-plot design as an example it is illustrated how these tests can be extended to more complex ANOVA models. In order to derive the test statistics and their approximate null distributions, Hasse diagrams for representing the structure of the experiment are combined with a stochastic process perspective. The application of the more general F-type tests is illustrated for simulated data.