MATCHED REEXPRESSION FOR PRESENTATION OF TRANSFORMED DATA IN LINEAR-MODELS

Emerson and Stoto, elaborating on a suggestion of Tukey, suggested making comparisons between members of a family of transformations {f(i)(y)} by transforming to the scale x(i) = a(i) + b(i)f(i)(y). Suitable estimates of a(i) and b(i) can be found for each f(i) to make the scales of x(i) and y agree at one or possibly two points. Such a linear rescaling of a transformation, or matched re-expression, can be usefully adapted to the presentation of results of multifactorial experiments designed to test hypotheses. This allows the presentation of means on the scale of the analysis which are also in a range of values which is familiar to the experimenter. Generalized linear models may be similarly presented. Examples from four experiments illustrate some of the possibilities and problems of this approach.