Data Analysis Using Reconstructability Theory.

Abstract

In this dissertation, we develop a new data analysis method using reconstructability theory, particularly k-systems theory. K-systems or Klir systems theory is a branch of reconstructability theory and provides a setting wherein common problems in statistics can be solved using the power of information theory by invoking the maximum entropy principle. The method is superior over classical statistical data analysis. The approach starts with the concept of variable interaction in reconstructability analysis (RA), We then use the RA definition of interaction to improve the quality of main and interaction effects in data analysis. With classical statistical data analysis, we need to assume a model for the data and then check the validity of the model using such techniques as plotting residuals. Questions arise not only on how the model relates to the underlying data but also on the relevance of the assumptions which accompany the model. If these assumptions are grossly violated, the procedures used to draw inferences about the model may be invalid. Our method overcomes this problem. Unlike classical statistical data analysis, our method assumes no model for the data and works directly with whatever information is available in the data. Thus, no model validity checking or assumption verification is needed. In addition, the results obtained are valid and true for the given data. The method has been used to analyze real experimental design data.