One purpose of data transformation is to better satisfy the fundamental assumptions of statistical analysis by linear models: (a) additivity, (b) homogeneity of variance, and (c) normality. If the original data do not satisfy these assumptions, a nonlinear transformation may improve approximation to these ideal conditions. This paper considers estimation of the parameter lambda of the family of power transformations for data conforming to a replicated two-way crossed classification. Two procedures for choosing a transformation for data from a replicated two-way crossed classification are compared by empirical sampling: One, proposed by Box and Cox (1964), is based upon the likelihood of the transformed observations; the second, proposed in this paper, is a linear combination of test statistics for removable nonadditivity and variance trending with mean. Two cases of empirical sampling from a 3 x 4 crossed classification with four replications were studied.
