Eamples for types of multiple randomizations

Multitiered experiments are not a fundamentally new class of experiments, but are a drawing together of existing experiments that have in common that they involve multiple randomizations. They can be classified according to the types of multiple randomizations or according to kind of experiment that is involved. Below are examples for the six different types of multiple randomizations, composed, randomized-inclusive, unrandomized-inclusive, coincident, double and independent, as well as for experiments that involve three or more randomizations.

Composed randomizations

Tobacco mosaic virus experiment (McIntyre, 1955), Cotton fibre experiment (Cox, 1958, Example 3.2); Brien and Bailey, 2006, Example 4), Drug-testing experiment (White, 1975, example 2), Simple sensory experiment (Brien, 1983; Brien and Bailey, 2006, Example 1), Wine sensory experiments (Brien, May and Mayo, 1987), Horticultural experiment (Preece, 1991)), Meatloaf tasting experiment, Corn seed germination experiment (Brien and Bailey, 2006, Example 12; 2010, Example 5), Continuous grazing experiment (Brien and Bailey, 2006, Example 3), Nonorthogonal sensory experiment (Brien and Bailey, 2006, Example 15; Brien and Bailey, 2010, Example 2).

Randomized-inclusive randomizations

Wheat experiment (Brien and Bailey, 2006, Example 9; Brien and Bailey, 2009, Example 4), Duplicated wheat experiment, Potato storage experiment (Brien and Bailey, 2006, Example 13), Knitted sock experiment (Brien and Bailey, 2006, Example 14), Rotational grazing experiment (Brien and Bailey, 2006, Example 8; Brien and Bailey, 2010, Example 4), Artificial example (Wood, Williams and Speed, 1988).

Unrandomized-inclusive randomizations

Superimposed experiment using a row-column design (Brien and Bailey, 2006, Example 10; Brien and Bailey, 2010, Example 1), Potato storage experiment (Brien and Bailey, 2006, Example 13).

Coincident randomizations

A plant experiment (Brien and Bailey, 2006, Example 5; Brien and Bailey, 2010, Example 3), Corn seed germination experiment (Brien and Bailey, 2006, Example 12; 2010, Example 5), Laundry experiments (Miller, 1997; Semiconductor fabrication experiments (Mee and Bates, 1998).

Double randomizations

Rotational grazing experiment (Brien and Bailey, 2006, Example 8; Brien and Bailey, 2010, Example 4), Paired human-interaction experiment (Lewis, 2006; Brien and Bailey, 2006, Reply to discussion Figure 28).

Independent randomizations

A superimposed experiment using split plots (Brien and Bailey, 2006, Example 6), Human-computer experiment (Brien and Bailey, 2006, Example 7), Paired human-interaction experiment (Lewis, 2006; Brien and Bailey, 2006, Reply to discussion Figure 28).

Three or more randomizations

Corn seed germination experiment (Brien and Bailey, 2006, Example 12; 2010, Example 5), Potato storage experiment (Brien and Bailey, 2006, Example 13), Knitted socks experiment (Brien and Bailey, 2006, Example 14)