Transformations of Count Data for Tests of Interaction in Factorial and Split-Plot Experiments

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Abstract:

In applied entomological experiments, when the response is a count-type variable, certain transformation remedies such as the square root, logarithm (log), or rank transformation are often used to normalize data before analysis of variance. In this study, we examine the usefulness of these transformations by reanalyzing field-collected data from a split-plot experiment and by performing a more comprehensive simulation study of factorial and split-plot experiments. For field-collected data, significant interactions were dependent upon the type of transformation. For the simulation study, Poisson distributed errors were used for a 2 by 2 factorial arrangement, in both randomized complete block and split-plot settings. Various sizes of main effects were induced, and type I error rates and powers of the tests for interaction were examined for the raw response values, log-, square root-, and rank-transformed responses. The aligned rank transformation also was investigated because it has been shown to perform well in testing interactions in factorial arrangements. We found that for testing interactions, the untransformed response and the aligned rank response performed best (preserved nominal type I error rates), whereas the other transformations had inflated error rates when main effects were present. No evaluations of the tests for main effects or simple effects have been conducted. Potentially these transformations will still be necessary when performing these tests.

Keywords: data transformation; experimental analyses; factorial arrangements

Document Type: Research Article

DOI: http://dx.doi.org/10.1603/0022-0493-99.3.1002

Publication date: June 1, 2006

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  • Journal of Economic Entomology is published bimonthly in February, April, June, August, October, and December. The journal publishes articles on the economic significance of insects and is divided into the following sections: apiculture & social insects; arthropods in relation to plant disease; forum; insecticide resistance and resistance management; ecotoxicology; biological and microbial control; ecology and behavior; sampling and biostatistics; household and structural insects; medical entomology; molecular entomology; veterinary entomology; forest entomology; horticultural entomology; field and forage crops, and small grains; stored-product; commodity treatment and quarantine entomology; and plant resistance. In addition to research papers, Journal of Economic Entomology publishes Letters to the Editor, interpretive articles in a Forum section, Short Communications, Rapid Communications, and Book Reviews.
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