K-SYSTEMS VERSUS CLASSICAL MULTIVARIATE SYSTEMS

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Abstract
K-systems exist in general systems theory for the study of the relationships between parts and wholes. We show here that K-systems analysis can be used to solve problems in classical multivariate analysis, and solve them more effectively than existing methods. To demonstrate this, we take on “the analysis of variance” in this paper. The analysis of variance is the most important and powerful technique in the field of statistical inference (quoted from Probability and Statistics by Hines and Montgomery). We apply K-systems analysis to the analysis of variance problem, and we compare the two techniques. We see that K-systems analysis can provide more information. But the major difference is that the analysis of variance guesses a model for the data whereas K-systems analysis uses “the” model that is true and correct for the data. Further, K-systems theory delivers a surprising and important insight: it is generally incorrect to use any model where effects and interactions are represented statically over subsets of the equations (as in the analysis of variance). Not only is the K-system the correct model, but any other model assumed by the user is almost certainly wrong. Despite the complexities which they capture, K-systems deliver results in a clear, simple, and strong way.

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