Was This in Your Statistics Textbook? V. Transformation of Data

Summary

Additivity, variance homogeneity, and normality are often regarded as prerequisites for analysis of variance. Although they are desirable, their truth is never certain; they are important to probability levels in significance tests, but not to the general informativeness of the analysis. Transformation of data may improve conformity to these desiderata at the cost of producing results on a scale ill-suited to the objectives of the experiment. In this paper the generalized power transformation and the inverse sine transformation are described, and the practical problems of choosing an optimal transformation discussed. An ideal choice can seldom be based on the evidence of one experiment, and adopting the same transformation for a series of similar experiments is usually more helpful than a search for the ‘best’. Warnings are given about inappropriate guides to the choice of transformation. In some experiments, separate analyses for two or more obviously distinct sets of treatments may be more rewarding than any attempt to find a transformation that will enable all to be handled at once. When one or two treatments (or treatment combinations in a factorial experiment) show data wildly out of line with all others, consideration of reasons should precede and possibly replace any approach through transformation. A sound general principle is that data are usually most clearly interpreted on the original scale of measurement. Therefore, transformations should be avoided unless clearly necessary; by this advice, I do not imply prohibition. Finally, attention must be given to the presentation of results; the most effective presentation does not necessarily employ a transformation or other special device adopted earlier in a statistical analysis.