Statistical analysis of modified complete randomized designs:applications to chemo-orientation studies

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Abstract
Often experimental scientists employ a Randomized Complete Block Design (RCBD) to study the effect of treatments on different subjects. Under a `complete randomization', the order of the apparatus setups within each block, including all replications of each treatment across all subjects, is completely randomized. However, in many experimental settings complete randomization is impractical due to the cost involved in re-adjusting the device to administer a new treatment. One typically resorts to a type of `restricted randomization', in which multiple subjects are tested under each treatment before the apparatus is re-adjusted. The order of the treatments as well as the assignment of subjects to each block are random. If the data obtained under any type of restricted randomization are treated as if the data were collected under an RCBD with complete randomization within each block, then there is potential to increase the risk of false positives (Type I error). This is of concern to animal orientation studies and other areas such as chemical ecology where it is impractical to reset the experimental device for each subject tested. The goal of the research presented in this article is twofold: (1) to demonstrate the consequences of constructing an F-statistic based on a mean square error for testing the significance of treatment effects under the restricted randomization; (2) to describe an alternative method, based on split-plot analysis of variance, to analyze designed experiments that yield better power under the restricted randomization. The statistical analyses of simulated experiments and data involving virgin male Periplaneta americana substantiate the benefits of the alternative approach under the restricted randomization. The methodology and analysis employed for the simulated experiment is equally applicable to any organism or artificial agent tested under a restricted randomization protocol.

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