Multiple Randomizations

Abstract

Summary. Multitiered experiments are characterized by involving multiple randomizations, in a sense that we make explicit. We compare and contrast six types of multiple randomizations, using a wide range of examples, and discuss their use in designing experiments. We outline a system of describing the randomizations in terms of sets of objects, their associated tiers and the factor nesting, using randomization diagrams, which give a convenient and readily assimilated summary of an experiment's randomization. We also indicate how to formulate a randomization-based mixed model for the analysis of data from such experiments.

Accounting for variation in designing greenhouse experiments with special reference to greenhouses containing plants on conveyor systems

“…The allocations shown are coincident [19] in that, in the allocations of pots and treatments to carts, both Tactics and the four combinations of Sides and Blocks are assigned to the Zones.…”

“…After 18 days they were transferred to the Smarthouse for the remainder of the experiment, where the pots were placed in carts arranged in 4 zones each of which initially consisted of 3 lanes by 24 positions. Thus the experiment is two phase [19]: a first phase in a greenhouse and a second phase in a Smarthouse. In the Smarthouse phase, the plants in a zone were subjected to one of the following four tactics:…”

Statistics for proteomics: Experimental design and 2-DE differential analysis

“…Thus, variability arises generally from both phases, calling for rational implementation of work plans [17,18]. It should be emphasized that establishing an experimental design allows bias reduction and increased confidence in experimental results.…”

“…This experiment thus calls for a randomization for both phases [18]. The schema of the experimental design is shown in Fig.…”

“…The block effects in the experimental design have to be taken into account in the modeling [10,[17][18][19]21]. Let us consider the example given by Design 2 of Fig.…”