A method of determining estimable functions and testable hypotheses in experimental design

Abstract

Applications of the general linear model in experimental design and analysis usually involve design matrices of less than full column rank. This may present a problem in determining what elements and functions of the parameter vector are estimable and what hypotheses are testable. This thesis discusses two methods of answering questions about estimability and testability, where the form of the design matrix determines the method to be used. The two methods, both of which can use computer routines, are: (1) direct mathematical computational approach, and (2) a modification of an analysis of variance routine, with a special case of this method using a modified ANOVA routine and solutions to systems of linear equations. Confounding of effects is developed mathematically in connection with determining estimable functions. Methods discussed in this thesis can be applied to the area of Army Test and Evaluation.