Choosing a transformation

The emphasis in the literature is on normalizing transformations, despite the greater importance of the homogeneity of variance in analysis. A strategy for a choice of variance-stabilizing transformation is suggested. The relevant component of variation must be identified and, when this is not within-subject variation, a major explanatory variable must also be selected to subdivide the data. A plot of group standard deviation against group mean, or log standard deviation against log mean, may identify a simple power transformation or shifted log transformation. In other cases, within the shifted Box-Cox family of transformations, a contour plot to show the region of minimum heterogeneity defined by an appropriate index is proposed to enable an informed choice of transformation. If used in conjunction with the maximum-likelihood contour plot for the normalizing transformation, then it is possible to assess whether or not there exists a transformation that satisfies both criteria.