Publication Date


Document Type


First Advisor

Gupta, Sudhir, 1953-

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences


Biological assay--Mathematics; Block designs; Biomathematics


A systematic approach to constructing the contrasts of interest for a biological experiment is obtained by the use of orthogonal polynomials. In completely randomized and randomized block designs no difficulty arises in partitioning between dose sum of squares into single degrees of freedom allocated to the contrasts representing preparations, linearity, deviation from parallelism, quadratic qurvature, deviation from quadratic curvature and so forth depending on the number of doses in the experiment. In incomplete block designs the contrasts of interest are taken to be eigenvectors of the C matrix in order to partition the adjusted treatment sum of squares. The C matrix is obtained from the intra-block normal equations, Q=Ct. Results on the C matrix along with its spectral decomposition and the Moore- Penrose generalized inverse are given. The incomplete block design is then balanced in such a way that the variances of all the elementary contrasts are equal. However, in biological assays three particular contrasts, preparations, linearity, and deviation from parallelism are more important than the others, hence are estimated with full or a higher efficiency. Different methods of constructing designs where these three contrasts are unconfounded are then summarized.


v, 73 pages




Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type