Esquemas de associação e delineamentos experimentais

Abstract

An important area of Statistics is that which studies experimental designs. Experimental designs refer to the design in which experiments are conducted. The mathematical theory underlying the construction of these designs is often little explained. An approach that presents in a balanced way the statistical analysis of experimental designs and also the complexity of the mathematics involved can be found in the works of Rosemary A. Bailey. The present work aims to clarify and make more accessible the relationship between Statistics and the underlying Mathematical Theory. In particular, the theory of association schemes and its connection with experimental designs. Hasse diagrams and their relationships with variance analysis are exemplified. The use of graphs in designs, a relatively recent theory in the literature, is also addressed. In this context, the present work aims to address the theory of experimental designs using association schemes. From this approach, we have the following contributions: a geometric example for the cyclic association scheme is proposed; a new algorithm for calculating the strata of a design is shown in detail; a discussion is presented on the different definitions of orthogonal designs; using graph theory, we have results on soluble designs; and graphs are used as electrical networks in optimal designs. Furthermore, some new alternative demonstrations are presented.