CONSTRUCTION OF BALANCED INCOMPLETE SEQUENCE CROSSOVER DESIGNS FOR FIRST ORDER RESIDUAL EFFECT
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Date
2021-04
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UNIVERSITY OF ILORIN
Abstract
Crossover design is a repeated measurements design in which individual subjects receives different
sequences of treatments (t) during the different time period one at a time with object of studying differences
between individual treatments. It has been found useful in several fields of research, among which are clinical
trials and nutrition experiments involving dairy cattle .A noticeable feature of crossover design is that it
leaves direct and carryover effects which is the effect of a treatment from previous time period on the response
at the current time period in the succeeding periods. A design method that can generate designs for a large
number of treatments is a challenge to researchers. Therefore, the aim of this study is to obtain method of
construction of designs for a greater number of treatments. The objectives of this study were to: (i) determine
prime numbers that satisfy primitive roots, x = 2 and 3 ; (ii) modify a construction method for balanced
incomplete sequence crossover design for prime numbers for primitive root 2 = x ; (iii) construct a new
class of balanced incomplete sequence crossover design for primitive roots 2 = x and 3; and (iv) use data
set to validate the modified construction method.
A universally optimal Balanced Incomplete Sequence Crossover Design (BISCOD) for first order residual
effect with parameter n (experimental units), t (number of treatments) and k (number of treatment in each
experimental units or number of periods) was constructed in this study. This is to enhance the estimation of
residual effect over class of design in which no treatment was allocated more than once on each subject, equal
replications for all treatments in the first p-1 period and each treatment preceded each other treatment (k-1)
times. A method of design that satisfies primitive root 2 = x and a proposed method that satisfies primitive
roots x = 2 and 3 were obtained through balanced incomplete block design.
The findings of the study were that:
i. prime numbers that satisfied primitive roots 2 = x and 3 included 5, 7,11, 13,17, 19, 37, 61
ii. design using a modified construction method were generated for all prime number of treatments
for primitive root x = 2;
iii. a construction method generates all prime number of treatments that satisfied primitive roots
x = 2 and 3 was developed; and
iv. modified design construction method was validated
The study concluded that the modified method performed better in terms of generated designs for a greater
number of treatments than existing method. The set of data from experiment of the crossover type was
validated. The study recommended that the modified construction generated be used for prime numbers that
satisfy primitive roots x = 2 and 3
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Keywords
BALANCED, INCOMPLETE, SEQUENCE CROSSOVER DESIGNS, FIRST ORDER RESIDUAL EFFECT