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Abstract

When it is desired to measure the residual effects and the number of treatments is odd, it is recommended that a combination of at least two Latin-square designs should be used; an extra refinement is to introduce an extra period in order to arrive at a design balanced for residual effects. The final design, therefore, becomes cumbersome and may prove to be a great hindrance in the practical execution of the experiment.

Here we consider single Latin-squares with the object of determining the most efficient of these designs, which when applied on their own produce optimum results.

A number of Latin-square designs having different patterns have been studied with the assumption that the residual effects do not persist beyond the following period. A method for the
estimation of parameter effects, i.e. Period, Subject, Treatment direct and Treatment residual effects, including the cases when residual effects persist beyond the following period, has been developed. The efficiency of these designs based on minimum average variance of the differences between two estimates and minimum variance of linear components of treatment as well as residual effects has been investigated.

Further study on the optimality of the designs has been made by applying the D-optimality test, which states that the mode efficient design has the maximum determinant of X X, where X is the matrix of independent variables at which a response is measured from the model, or equivalently has its generalised variance determinant (MATHMATICAL EQUATION, UNABLE TO FORMAT. PEASE READ ABSTRACT ON PDF) minimum.

The pattern of the most efficient Latin-square design has been established along with a method to generate such designs.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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