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Data Transformation in Two-Way Analysis of Variance ANOVA

Schlesselman, James J.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
National Science Foundation (NSF), Office of Naval Research, Analysis of Variance (ANOVA), Mathematical Models, Statistical Analysis


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.

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