JSM 2005 - Toronto

Abstract #302852

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Activity Number: 200
Type: Contributed
Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
Sponsor: General Methodology
Abstract - #302852
Title: On Transformations of Count Data for Tests of Interaction in Factorial and Split-plot Experiments
Author(s): Mark Payton*+ and Scott J. Richter
Companies: Oklahoma State University and University of North Carolina, Greensboro
Address: Department of Statistics, Stillwater, OK, 74078-1056, United States
Keywords: Count data ; Split Unit Experiments ; Aligned Rank ; Interaction
Abstract:

When a response is a count-type variable, certain transformation remedies are commonly employed. Most common among them are the square root, log, and rank transformations. This study examines the use of these transformations in factorial or split-unit experiments with a simulation study. Poisson-distributed errors are used for a 2x2 factorial arrangement in both randomized complete block and split-plot settings. Various sizes of main effects are induced, and type I error rates and powers of the tests for interaction are examined for the raw response values, log, square root, and rank transformed responses. The aligned rank transformation is investigated as it has been shown to perform well in testing interactions in factorial arrangements. We found that for testing interactions, the untransformed response and aligned rank response performed best (preserved nominal type I error rates), while the other transformations had inflated error rates when main effects were present.

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