ABSTRACT
In this chapter, the author aim to prepare the way for a variety of diagnostic coefficients, one class seeking better homogeneity of variability, one class seeking less non-additivity, one class seeking better linearity of response. They show that the goals are much more often co-operative than conflicting. Removable non-additivity, for example, is hard to detect unless at least two factors have substantial effects, because its consequences are then small. Removable non-additivity and removable non-linearity may be greater issues because they directly affect the primary results of the analysis, typically estimates of individual behaviour. Removable inhomogeneity of variance is typically more important in assessing, more correctly, the uncertainties of such primary results than it is in improving the precision with which the primary results are assessed. A particularly important advantage of using matched re-expression is that it overcomes the need to back-transform to the original measurement scale.
