Multitiered experiments

Multitiered experiments are experiments that involve more than one randomization, where we are specific about how a randomization is defined. As they involve multiple - two or more - randomizations they have more than two tiers, and hence are multitiered. They differ from the majority of textbook designs, including split-plots designs, as these involve a single randomization and so are only two-tiered.

Multitiered experiments are not a new set of experimental designs. They are a class of existing experiments that have in common that they involve two or more randomizations. They include two-phase, some superimposed, many animal and some plant experiments. Examples of multitiered experiments are available from the Examples menu.

Six types of multiple randomization, summarized in the following diagrams, have been identified: composed, randomized-inclusive, unrandomized-inclusive, coincident, double and independent. Note that composed, randomized-inclusive and unrandomized-inclusive randomizations are similar to the extent that there is left-to-right randomization of the three tiers. However, they differ in the relationship between the two randomizations involved. The two composed randomizations are independent, whereas randomized-inclusive and unrandomized-inclusive randomizations take the result of the first randomization and either randomize it or randomize to it. Also, coincident and independent randomizations are similar in that they both randomize to the same set of objects. For coincident randomizations, the two randomizations have some of the same generalized factors to which factors are randomized, whereas for independent randomizations they do not.

Definition; Examples
Definition; Examples
  • Used where all information from each randomized term is to be confounded with the same term(s) and neither randomization needs information from the outcome of the other.
  • Occurs in two-phase experiments and grazing trials.
  • Used where two terms from different randomizations are to be confounded with the same term(s), and hence with each other, e.g. when treatments introduced in a laboratory phase and replicates from a field phase are to be confounded with same laboratory phase terms.
  • Occurs in a range of experiments including two-phase, single-stage and multistage same-unit experiments.
Randomized inclusive
Definition; Examples
Definition; Examples
  • Used where information from a term is to be subdivided according to results of a first randomization and different parts are to be confounded with different terms.
  • Occurs in two-phase and multistage same-unit experiments.
  • Used where a generalized factor is to be randomized twice.
  • Occurs in rotational grazing trials and human-interaction experiments.
Unrandomized inclusive
Definition; Examples
Definition; Examples
  • Used where unrandomized factors for second randomization have to take into account the assignment all factors from first randomization.
  • Occurs in some superimposed experiments and two-phase experiments.