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.

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This note sketches a biological context for the negative binomial distribution, gives some of the many equivalent mathematical notations that have been used for the negative binomial probabilities, and discusses the use of the computer program MLP (the Maximum Likelihood Program) for fitting negative binomial distributions to data.