Models, Transformations of Scale, and Weighting

Abstract

A realistic model is an indispensable prerequisite to any meaningful data analysis. Since most common statistical procedures are based on models involving specific assumptions, such as homoscedasticity or absence of certain interactions, it has become current practice to transform the scale of the data in the hope of achieving conformance with these assumptions. It is suggested in this paper that this approach is logically unsatisfactory. The conclusions drawn from a meaningful analysis should be essentially invariant with respect to scale transformations. The model should be flexible enough to allow for a realistic representation of the physical reality underlying the data. Heteroscedasticity should be dealt with by means of statistical weighting, and interactions, rather than being “assumed away,” must be part of the model.

The proposed approach is shown to satisfy these requirements and is illustrated in terms of two individual studies. One is an interlaboratory evaluation of a physical test procedure and the other one deals with the within- and between-laboratory precision of a method of chemical analysis.

• Transformations of Scale
• Weighting

Additional information

Notes on contributors

John Mandel

Dr. John Mandel, statistical consultant to the Institute for Materials Research of the National Bureau of Standards, is a fellow of the ASQC, ASA, Royal Statistical Society, and AAAS. He has taught at Rutgers University and is an instructor of courses sponsored by the ASQC Chemical Division. He won the Frank Wilcoxon Prize in 1971 and was awarded the Gold Medal of the U.S. Department of Commerce in 1973.