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.

We specify an algorithm to enumerate a minimum complete set of combinatorially non-isomorphic orthogonal arrays of given strength t, run-size N, and level-numbers of the factors. The algorithm is the first one handling general mixed-level and pure-level cases. Using an implementation in C, we generate most non-trivial series for t = 2, N ≤ 28, t = 3, N ≤ 64, and t = 4, N ≤ 168. The exceptions define limiting run-sizes for which the algorithm returns complete sets in a reasonable amount of time. q

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Many conditions of the RAPD reaction procedure may influence the result. This paper presents rapid detection of influential factors with a fractional factorial experiment. A more extensive study of these factors is also presented. Polymerase brand, thermal cycler brand, annealing temperature, and primer, are important factors in obtaining good DNA yields and optimal fragment patterns. Each primer has its optimal annealing temperature, and this is not correlated with the GC content of the primer. Optimal species-primer combinations have to be found by trial and error.

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