  Hasse diagrams provide a principled means for visualizing the structure of
statistical designs constructed by crossing and nesting of experimental
factors. They have long been applied for automated construction of linear
models and their associated linear subspaces for complex designs. Here, we
argue that they could also provide a central component for planning and
teaching introductory or service courses in experimental design.
  Specifically, we show how Hasse diagrams allow constructing most elementary
designs and finding many of their properties, such as degrees of freedom, error
strata, experimental units and denominators for F-tests. Linear (mixed) models
for analysis directly correspond to the diagrams, which facilitates both
defining a model and specifying it in statistical software. We demonstrate how
instructors can seamlessly use Hasse diagrams to construct designs by combining
simple unit- and treatment structures, identify pseudo-replication, and discuss
a design's randomization, unit-treatment versus treatment-treatment
interactions, or complete confounding. These features commend Hasse diagrams as
a powerful tool for unifying ideas and concepts.
