Exploratory Methods for Choosing Power Transformations

Abstract
Power transformations can often simplify the task of describing behavior in data that consist of positive measurements or counts. Tukey's diagnostic techniques based on two-dimensional plots are useful in searching for a suitable transformation in two types of data structures: multiple batches at different levels, and two-way tables. To these, we add plots for finding transformations in two other structures: a single batch, and y versus x. The basis for plots that indicate transformations for symmetrizing and for straightening is explored using second-order series approximations. For all four techniques, when the plot is roughly linear with slope 1 — p, the power of a transformation indicated by the plot is p. Each plot indicates whether any power transformation can be effective in achieving a desired objective.